nezaj. Včešče in vse, da se je vse zespečen, z tem, da je vse zespečen, od vsez, v korišu, in vsez, da je vsez, in vsez, da je vsez, koriš, in vsez, da je vsez, ta vse svojstje koukaj skupaj je sezdano. Početno štef, da je to vsi zelo, da je to tako zelo začostil. Našli vse se je zelo, da so možemo pokazati, da je to vsezdano v konfliktim kanonijstvom, zelo pošli, da je to vsezdano vsezdano. zitebenي, kajavingi dva vsi, in potem topoti z vsi o tudi z ateptikimi zesefati, zalojte to dorge v universalnih properti in v glasbi proprtiti vsi, počusi imam vsi basen, tudi počuti vsačega.    Vsi nekaj modeli se občajati vse unijersalno modeli, z kajom vsečenem vsečenem vsečenem vsečenem vsečenem, kaj je unijerno vsečenem. Tudi je unijda vsečenja. Unijda je argument, ker to bude rezentabilitiv, kar naredzana kaj je to prostavi, ki je to doj rača, JT gleda domovesti. Na pé veliko stvari, ne igre taj sem sprejden, tako moment strana, kako ta je, bo izgvorega včet04 način je to blizna, na častrojno Efrije, compt忌, stvar. In zelo, da se nesetak je zelo, da ne zelo, da je nezelo, da se tako je zelo. Zelo je, da je dobro. Zelo, da se nezelo, da se nezelo, da se nezelo. To je po vseh vseh opozitivnih. To je nezelo. Tak, tak.  Uvršen je, mt. Tudi mt je vzelo prejderzaj taktiko in pr carry buljaca, imaš zelo, da také, kako Ingrediente mežije na topolo, je to, da dogažujš, v kratku zrani v posledu. Tuk,,, tudno je take, ki je vse tako kona, kot se najmega je, kako je tega, ki ne je, kaj je to? Tako, je to, če je, da razprvamo in je, če je, gaj, si je občasno this model there, nared nared, in so what you get is that this angle will be azo-mortific to angle will be azo-mortific to. Eštečne. So this picture shows you that, basically, this is sort of a center of symmetry of the theory because everything that happens elsewhere, in some sense is deformation včoč, da se pravno prišljamo v točko, če pričo seznačnih vsemačnjih, kot vseznačnjih, zato se zelo, že v twentvoj modelu, katera je večo objavna, katera je vseznačnja. Jeste tako vseznačne kompletnosti, da je zelo izredalja iz toj model. OK, zato je je vseznačna pristim vseznačnja, In vseč, naredite je mnogo, da ne jste ne zelo. To je modem, je modem od... V moji modu, na različenju, majske mode, ne bo modem, ne bo modem. Zato je, da bo, da bo, da bo, da bo, da bo modem.  Zato, da so posledili toga vsemo, da bi bomo zelo tudi sega, da so tudi zelo, da bomo zelo, da so tudi zelo, da bomo zelo. Zato, da smo pričeli ti način, da se obšihamo, da vseh je tudi vsega vsega vsega vsega tega vsega. vsega trijna z vsem.   In to, da se pridrečno sem, da se je prijezena pri teba na vsega klasik. Vse je tudi vsega vsega klasik. Vsega je vsega klasik. Tudi je to vsi kategorije, a zato je to vsega zelo. Ovo, kako je to prijezena? Tukaj, da je ta vsega? Nelj, kako je je zelo? Asositi štefnike razičiljajoveda o dogrom construjnji, dogrom studiarcije, navr Address, so izgledamo to, da je tega. T and t prime are set morita equivalent in observacije. in ki sem tukaj v equivalentnih klasitarnoj, to je tukaj pravda definitiva. To je nekaj in nekaj, da je tega vzgleda, in zelo, da je vzgleda na to, ker je tukaj, klasitarnoj, in tukaj vzgleda na vzgleda, da se poču, da se poču, da je vzgleda na vzgleda na vzgleda, in je zelo, T gay, shouldn't see it later. But I just to say that this is really a strict generalization of the notion of War-Clinker and targ of the classical one. Okay, so, this means that we can identify growth and ectoposis with geometric theories considered up to war with equivalence. And so the bridges that I would like to talk about vseč potrebno o časneje, da se može izgleda, da imajo dva teori, ki se izgleda, tudi tako greba, po transparati vsi z odku in odkorti.  Kaj je tega nekaj vzvečenja, da vseznačenje je nekaj nekaj vzvečenja, zelo je nekaj nekaj nekaj vzvečenja vzvečenju bih komersi, da je dobrozne. Zelo bih komersi ima, da bom je vzvečenja, the usual formula is in the language of the force theory to to translates in the language of the second in a way that this induces an equivalence of the semantic level. So there are many, many examples, of theories that are not Certified but that are equally equivalent. So in those situations you don't have additionally so you cannot perform a direct translation between the two theories but the fact that the two theories share the same classification of those means pa nekaj ne bo, da sem se zelo početila. Zato, da je pa različila, da se početila, da se zelo početila, in zelo početila, da je to več načinčno.  Začelim, da se istradi, da zelo veče več vzdučnje, ker, zato vzdučnje, zelo vzdučnje in vzdučnje, vzdučnje vzdučnje, became, then when you look at these operations from the point of view of fear, you often find things that are very interesting, I will start with a very simple invariant notion, which is the notion of subtropos and I will describe how this notion expresses in terms of logic, which is logical countert art of the notion of subtropos. Tukaj je to rezultat, ko sem vzela v moj tizijskih. Če sem tukaj vzela geometričnih teori, je tukaj klasika in opos, sem tukaj na definicijs, ker sem tukaj nekaj... Zato, nekaj je tukaj vzela o težko, zelo, da bi se počuče definicije. Kaj je to tukaj, tukaj nekaj, je je počut, nekaj je tukaj, tukaj je tukaj geometrična inkluzja. So it is a geometric morphism, such that it's a direct image is full and taken. What is a quotient of a geometric theory while it is simply a theory which is obtained from the given theory just by adding more axioms while remaining over the same signature. So you don't change the signature, you just add more axioms. And what is a syntactic equivalence while it is the reaction that identify the two theories over the same signature when they prove exactly the same geometric sequence. To change the set by so much, the theory remains the same. Yes, exactly.  Because, of course, I mean, if you add the things that are provable, the models do not change, so you certainly cannot expect this to hold. And so this bijection works in the following way. So when you have a quotient of t prime, a quotient of t, so here you will have the universal property of the classified topos of t, which gives this. And then you can write something analogous for t prime and t diagram, where here you compose with this inclusion and given by the subtopos. So in particular, the domain of the subtopos will be a classified topos of the quotient. So you really, you can localize everything in a most natural way. OK, so how does this work? Well, the proof is not particularly difficult. I will just give the idea. We just used the representation, the syntactic representation that we gave of the classified topos of the theory. So let's do this. You take shifts on the syntactic side and you use the fact that the notion of subtopos admits a very natural side characterization. When I say side characterization, I mean a way to describe this invariant in terms of the given side of the definition for the topos. So this means that when you consider subtopos of shifts in a certain side, this corresponds exactly to the grotes of topologies t prime on c, which contains to refine the topology j. Very natural thing. Yes, it means that to obtain j prime, starting from j, you just add more. And in fact already from this remark you can be more or less convinced about the truth of this result because here on one hand you add more shifts and on the side of logic you add more axioms. And in fact we shall see how to add little shifts on the other side. So more precisely here what we have is that we have a direct bijection between the grotes and topologies j which contain the syntactic topology and the quotients. So how does it work? So imagine that you have a quotient t prime so here it means that you have added axioms of this form for instance to your theory. You can go on the other side so here you have to know what to add to the syntactic topology and so here you just have to recall that flat, I mean here we just have a Cartesian Cartesian jt continues counters which yesterday remark did the same as the geometric counters this to any toposki the same thing as the models and this word in the following way a model was sent to the factor fm which sent any formula any geometric formula to this interpretation in n. So you have said that this is the same thing this of course and then you can consider this monomorphism in the syntactic category and basically requiring that this is sent by to an isomorphism by the factor fm precisely amounts to the condition that m should be a model for this additional sequence and so from this you get the idea of considering the growth in the topology generated by all the the sieves generated by things of this form and so this is how one direction is defined and the other direction well, yesterday we observed that we gave the definition of this syntactic topology you have a situation of this kind so if you have a we describe our sieves on this syntactic category well so let's just replace this and so starting from a sieve here you can be the sequence in the following way just take and so by adding all the sequence obtained in this way you will get your portion so I think it is pretty clear how it works of course there are some technical things to make the tool completely it goes back I think you should make the remark that it is not completely straight forward application of what you did yesterday because when you go from t to t prime their syntactic categories as defined yesterday are not the same in the sense that here we represent no, of course here basically I change the topology in the sense that I represent the classifying tools of t prime as she is on on this but we also know by the general construction of classifying tools that this is also equivalent to to this so you see that here we have a different category so I mean that you come all the time with multiple ways of representing the toposis in the sense of multiple size of definition for the same toposis it is very, very easy to generate different possibilities for describing the same tools OK, yeah describing the same group exactly, exactly I mean already Grotendick made this comparison he said that if we we think about this analogy group toposis then basically different sets different sizes of definition for one toposis can be in some sense a sort of analog of different presentations for the same group OK, so so quotient of t just means that you keep the same signature we just add more things over the signature and the formulas are course in geometric yes, always, always so if you do it with other fragments it's a very good question it's a very good question that I asked myself actually some years ago and this is very interesting because even if you start for instance with a theory that lies in a smaller fragment of geometric logic there is no intrinsic way of identifying only the sub-toposis that correspond to them so I mean there are some invariants for instance you can say that a toposis is coherent so the notion of coherence was already present in SGA4 and you can prove that a toposis is coherent if it is the classifying topos of some coherent theory but this is the only thing you have and this doesn't allow you to restrict the equivalence even by this duality to those fragments so this is interesting because it makes appear the fact that really geometric logic is the fragment that corresponds to the geometry of growth and decomposition so it means that if you decide for instance to restrict your attention to coherent toposis because maybe you like the assumption of choice and you are assured that they always have enough points when you perform operations which are as natural as the sub-topos construction you come out of that so you see this is an illustration of the fact that really the logic that corresponds to growth and decomposition is geometric logic and nothing else ok so now that we have this duality we can start playing with it because in the sense that we have another question at the site of 50 prime essentially you are just setting more atoms, the objects are the same but what I think yes the objects are the same what changes is the probability because probability in t prime or probability in t so you are less and essentially the sites will be the same because you are adding the sieve on a certain object if that sieve is a sequence derivable no you have a different notion of arrow because so it's a different category and you have a different notion of probability but what we see in the old one in the c t j for those in the old one should we say you get sieve I thought there could be new sieves that essentially are covered already by the one in the next what happens if you add contradictory actions well you can always do so in this way you get a contradictory theory and this is how can you have a model no it has no models you have a topos which has no models no points at all and which is trivial as a topos so no it's a very important feature of logic the fact of being able to talk about contradiction because I mean it's not I mean no no it's important it's like when one works with imagineries I mean you can add and then you will see whether it is contradictory or not but you add so the message of logic is don't worry add things and think like that yeah you say it has no model I might object because the degenerate topos will be a model in model yes I mean no at least no set that's the when usually in logic they say something has no model the logician means non-empty model yeah that's what it means but the case of the you have always been the degenerate topos no no you have this degenerate topos and you can really study it as an object and you can also prove for instance that the fear is not contradictory by showing that the topos is non degenerate I did this for instance in one of my papers so I really proved that the topos is non degenerate I knew for instance that this topos always had enough points and I was able to deduce that there was at least one point for instance so I proved the existence of one set based model of a theory using the degenerate topos for which set? well it was a theory of homogeneous models for certain theory of ancient type so it was a theories arising in the context of crisis construction so maybe I will say a bit about this later ok now let's come back to this duality so in this duality one last question if the theories maximum is complete what happens to the classifying topos well if it is complete in the sense of geometric logic it means that the classifying topos is too valuable and if this topos is also atomic which is something important to have because if you have atomicity or at least bovianess you can prove that the notion of completeness for geometric logic which means that any geometric assertion is either true or false in the theory this notion becomes equivalent to the first of the notion of completeness which is not generally the case for any geometric theory and for those theories like that these are maximal with respect to the natural order of theories that it is induced by this duality but I will come back to this because here of course the duality gives a lot of things because at the level of subtoposis you have many structures that you can consider in particular you have the order between subtoposes you can say one subtoposis including the other and so you can wonder what corresponds to the level of theories and so duality in order between theories you say two theories one is well, let's try it like this one is smaller than the other if this is a portion of that it means that everything is provable in tipa exactly exactly another way of saying it so we have an order in the level of geometric theories which are quotient of the given theory and knowledge of elementary topos theory applied to the lattice of subtoposis of the given topos tells us that this order is actually a niting algebra structure because at the level of subtoposis you have a co-hiting algebra structure so since you reverse the inclusion we get a niting algebra structure here so it means in particular that you have a join that you have a meet etc between theories and it sounds that you can even give a very explicit description of what these operations are you get an atomic height you get an atomic height because there are maximal theories yes you can almost it is almost it is not exactly but almost in the sense that for most theories you can find a maximal one that extends it for most so which operations are available on the collection of subtoposis you say that you have a join and a meet do you have infinite meet yeah you can also take that of course and do you have some kind of complement or this doesn't make sense yes you have this sub pseudo complement if you want this you always have when you have in a niting algebra do you have infinite joins also yes of course if you wanted to take here what you do at the level of logic you just put the actions of how do you define the join of two theories when you take the actions of the first the actions of the second and you put all of them together so you get certainly a new theory provided that it is a set so yes you can define is there a simple example of a geometric theory that does not admit maximal extension no but maybe I didn't think about this problem but I proved that in many situations I showed how you can get something maximal out of a theory with some properties but it depends also on which kind of set theoretic assumptions you want to make many choices yeah that's the point if you want to do things completely constructively then it can be a problem but with choice do you get the mathematical point? no, not even sure in many cases yes but I mean I repeat I haven't really addressed this completely but I can tell you that in most cases yes so you get this I think algebra structure so of course we have talked about the join you can take the myth so this is you take the things that are crucible in both and and from the fact that you have a co-writing algebra structure on the lattice of some topos you get also some nice properties of this like you have automatically distributivity for these operations etc so it's a nice thing to have and now I don't have the time to write down the specific externalizations for these operations but if you are interested you can find them in my paper so this is called the lattice for the moment my aim is not really to talk so much about logic but mostly about mathematics I mean the kind of insight on concrete mathematical structures that this duality can give so for instance well, just remaining on briefly on the subject of logic on the topospheric side you have the notion of open closed sub-topos and so these correspond to extensions of these kind so open sub-topos correspond to adding geometric sentences like that and the closed sub-toposis which are complements of these are given by sequence of these kind always in the empty context because these are geometric sentences so you can see it's very natural of the topospheric side and at the logical level another important construction that you can make in toposphere is the subjection-inclusion factorization of geometric morphism so what you can do is the following thing if you have a geometric morphism of toposis you can always factorize it as a subjection followed by a geometric inclusion of toposis so a subjection is a geometric morphism such that its inverse energy is painful so you always have this factorization it is a general result so you can look at what it is in the setting of the classifying topos of a theory because here you have sub-topos now it tells out that these sub-topos can be identified as the classifying topos of some theory which is related of course to this geometric morphism by the universal property of the classifying topos is the universal it is the geometric morphism corresponding to a model of the theory t in the topos here f and it tells out that this is the classifying topos of the theory of this model so you see it's very natural in logic to take all the things because we made an application of that even for non-remotives we used this kind of construction to take the theory of the model even though we did this in the context of regular logic just if you are interested this is the paper look I will probably mention this in this talk consider the theories of this in those paper and we showed that an appropriate version of the regular syntactic category of this theory yielded something that is equivalent to classical non-remotives so you see this is just to show that logic is really not a part from mathematics so it interacts very well with classical mathematical context sorry here I know what to say so here we have talked about open sub-topos and here about closed sub-topos we have also talked about the logical interpretation of this construction there are of course many other things to say for instance there are many constructions that you can make local operators that you can consider on a topos to produce sub-toposis so when you have a topos and you have a universal closure operation sub-objects so this means that you have a thing like this and there are some notable universal closure operations that one might want to consider for instance you can consider the double negation closure operator this gives what is called the booleanization of a topos so this is called booleanization it is a universal way of making a topos boolean and you had many other operations that you can construct sorry, have you well, you take for any sub-object you consider the double negation of that here the negation is the pseudo complement in the hiding algebra in which the sub-object is so the sub-object you had a hiding algebra of sub-object so you just take this and you take it two times and so you get something bigger so you define it in this way you operate in the lattice of sub-object of sub-object sub-object so so this is one example but of course there are many more and I mentioned this just because of the relevance that it has in the context of various national mathematical theories there is another construction that I introduced which apparently is very eccentric so basically I proved that given a topos there is always a large dense sub-topos satisfying the Morgan's law now I am not going to explain exactly what it means but just to show that apparently you see here we are talking about the Morgan's law on a topos so this suggests that in this hiding algebra sub-object of this law also and the demorganization is a sort of universal way of the topos demorgan and basically as you can see here you are doing completely topos theoretical considerations so apparently you don't expect that when you look at this thing under the mirror of the duality you will find meaningful examples in the context of particular mathematical theories but actually the reality is the opposite because for instance we proved with Peter Johnson that if we take the classifying topos for the theory of fields so a very simple and natural theory and we consider the demorganization of it then this corresponds under the duality to a very natural theory which is the theory of fields of finite characteristics which are algebraic over the prime field so you see this is I mentioned this just as an illustration of the fact that apparently weird and remote constructions that you can make here might give rise to naturally defined mathematical notions and here since I have talked about dualenization, what does it give in the context of the same theory when it gives the fields that are more over algebraically closed so you see you get really natural mathematical examples if you change the theory because you might think what is missing from the demorganization to dualenization no, the demorganization is bigger so when you take the dualenization you get smaller topos and this corresponds to taking the fields that are finite characteristics which are algebraic over the prime field and if you want to get the dualenization you have to add more over the condition that they are algebraic. but logically speaking the rule that is not satisfied by the demorganization but the law of excluded middle because here this is weaker than the law of excluded middle the law of excluded middle is this so this is a weakening it is an intermediate logic in whitenistic logic in classical logic but this law does not hold in general the first law does not hold in general no, no, not atrope this is why it really defines an intermediate class of toposis which are called demorganized toposis and so let's just change the theory to show that this fruitfulness for classical mathematical situations is just not completely by chance is not peculiar to that particular theory if you take the theory of linear orders for instance the dualenization gives the theory of dense linear orders without 10 points which is again a very natural theory ok, so this is just to give you an idea of the fact that this correspondence given by the theory of classifying toposis between geometric theory of one hand and growth in the toposis on the other is actually very, very natural so now let me move excuse me when you say that the theory of you consider the theory of fields as a geometric theory what do you mean? the usual first order? no, it is a coil you can formalize the theory of fields within coil and logic you can do it without changing the signature you do it in the signature of commutative rings within units so it becomes a portion of the theory of commutative rings within units ok, so now let us talk about theories let us talk about a class of theories that is particularly important in topos theory at least concerning the logical understanding of classifying toposis is the class of theories of pre-shift type the theories that are classified by pre-shift topos why are they interesting? well, simply because since every growth in the topos is a sub-topos of the pre-shift topos so you can expect every geometric theory to be a portion of a theory of pre-shift type this is actually true so basically theories of pre-shift type you can regard them as the basic logs from which you can construct any kind of geometric theory so in some sense these are the simplest theories that you might want to consider and all the others will be given by an addition of axiom to them so the definition is theory classified by a pre-shift topos so in principle you don't specify the kind of pre-shift topos that you might want but it turns out that this category here is essentially determined by the theory in the sense that if imagine that the tree is classified by such a topo then let's look at what it says at the level of the set-base models of the theory well it means that the flat topos like that but this is precisely the in the completion of the category C why? because flat functions are just the functions that are filtered co-limits of representables so this is basically the filtered limit filtered co-limit completion of the category C and it turns out that you can recover a scene from the in the completion by taking so scene up to C completion is equivalent to the category finally presentable objects of this category and so it's also finally presentable objects of yes so what is a finally present, yes to say so definition so well I will give it for a model but it is a general definition you say that it is finally presentable when in a category which has filtered co-limit when you consider the home function, the covariant home function and you require this to preserve filtered co-limit ok so this is so here we have so this means that when a theory of pre-shift type it is always classified by this because if you just take the co-ship completion of a category, the resulting category of pre-shifts does not change so you can directly take this and this gives the sort of canonical representation of the classifying purpose notice that yesterday we have already identified a subclass of the class of theories of pre-shift type namely the Cartesian theories because we showed remember that if t is Cartesian then you have that the classifying purpose is just take the Cartesian syntactic category of the theory and this is this classified by a pre-shift purpose so it is a theory of pre-shift type now the interesting thing is that this class is much much broader than the class of Cartesian theories because it includes many theories that are even infinitary whose syntactic form is completely different from that of Cartesian theories so I will give just a few examples so you can consider the theory of linear arms and for instance to consider to formalize the notion of linear order you need a disjunction because you have to specify that the order is total so you see we are no longer in the context of Cartesian logic or you can also consider the theory of intervals by interval I mean a linear order with bottom and top and this theory is interesting because it is classified by the topos of a simplicial set which is in fact a pre-shift topos we have many other examples so the theory of algebraic extensions on a given field this is an infinitary theory because if you want to express the algebraicity condition then you need an infinitary disjunction you have the theory of lattice order and a billion groups with a strong unit for instance the notion of strong unit also requires an infinitary disjunction over the natural numbers you also have Amin Alankone and Katja Konstani have used both the cyclic topos that Kon had introduced in the 80s and the more recent 80 cyclic topos these are two pre-shift topos and one can describe few result pre-shift type classified by these topos in a paper entitled cited theories if you are just curious to see what it gives they are relatively simple theories that one can describe but simple but not cartesian which are classified by these important topos and so I mean this is just to illustrate the fact that in some sense these theories form a huge class and so even though apparently in terms of syntax they look quite different from each other they share many properties because actually you can prove various reports about these class theories for instance a very natural question that you can ask about the theories of pre-shift type is what about the classical syntactic notion of finite presentability because I can define you see normally in universal algebra one defines a model to be finitely presented if there is actually a formula that presents this model while the definition that I gave here is completely semantic you just categorical you work in a category and then you require a normal function to wonder whether there is a relationship between this syntactic notion of finite presentability and the semantic one but let's give a definition so m is said to be is considered in the context geometric formula in context interpretation of this formula in any model n are in natural correspondence in the homomorphisms so you see this is for those of you who are familiar with the free structures this is a generalization because in the case of where you have two you just find the notion of free model and here we allow any possible geometric formula so you see we have this definition a significant difference between the two and actually you can realize that if a model is finitely presented with syntactic in this sense then it is also finitely presentable this is quite easy to show but the converse is by no means straight forward because imagine that you start from something that is finitely presentable in this semantic sense it is not a priori clear at all how to find a formula but we have a sort of special method to address this kind of problems a bridge technique which suggest us to work with multiple representations of the specificity of our feeling and so in the case of fields of pre-shift type this is very nice because we have on one end the classical syntactic representation and on the other end we have this semantic representation I say semantic because you see the notion of finite representability that I use here is the semantic one so I use this and I know that it is correct because we obtained this description of the classical entobos by using the semantic definition rather than the semantic one so I have that and now I try to play with and I put off if I want to embed this into here I can do this but of course it is going to be co-variant only or to sort of pass from here to here because you see we start with something we start with a finite representable model in the semantic sense and what we want to do is to find something here you see here is the formula so we want to go from there to there but it doesn't seem feasible to do it directly because we have no key so how to do so we start from M and we have our immediate embedding that allows us to regard M inside the classical entobos now we use the fact that because this is a pre-shift entobos the objects of this entobos of this form they are very special they are objects that are irreducible because it means an irreducible object in entobos so it means that whenever you have anything more thickening so you say that A is irreducible if whenever you have anything more thickening like this then the identity on A necessarily factors through one of these arrows so you see it is a very very strong condition it is not something that in fact it is a condition that characterizes exactly in entobos up to Koshi completion of course if the category is not Koshi complete then you could have a retract of something that also is irreducible without coming from the side but here you see we have a Koshi complete category so we know that this is irreducible then we can transfer it here so let's call the object that we get here A and so what we can do is we know that A is irreducible as well because of course irreducibility is invariant so I can look at it from the other point of view and what I am very tempted to do since I really want a formula well I don't yet know that A is a formula but I can certainly cover it with formulas because in every object in entobos of sheep this is a general fact I mean if you have totes of sheep on a site then if you take all the arrows from the representables when I say representables of course you have to apply the associative sheep kind to this representables but so I denoted like that A, J or C you make a C vary give a few more feet do you assume it's a chemical? no no no not at all no because you have this is a consequence of the fact that the level of the pre-ship totes every object is a collimit of so you just apply and you get no no you don't need so it means that I can certainly the things that come from the site in these formulas and and since we know that A is reducible well then we have such a factorization but this implies that this factorization is monique but it means therefore that A is a sub-object inside the distopos of something coming from the site and you can easily see that it must come from the site itself because this category is closed under sub-objects in the totes so we are done we have found the formula so you see in a completely indirect way and we would have never been able to do it in a direct way because you see we are really exploiting the geometry of the totes what if I try to do it by contradiction I say there is no such formula then I keep going and I contradict the fact I don't think I tried myself a bit before and then for me it was a big surprise to find this result just by playing with this I didn't believe at first but then I understood that in some sense this is really the right point of view you see it's very simple and sometimes you get in a simple way you get different results that even in particular cases you could not prove so this shows that the two notions are equivalent and this is going to be useful now for describing the quotient the classifying toposes of quotient theories of which type and this is useful and of course it gives us a way to get more semantic representations of those classifying toposes because so far we have just syntactic ways of building classifying toposes which in practice are not very useful unless you are just interested in logic but the advantage of working with theories of bishop type is that you can pretend in some sense this category of penalty presentable models is semantic even though it is not actually because I mean this correspondence you can formalize it as an equivalence between this and the full subcategory of the syntactic category on the irreducible formulas what do I mean by irreducible formula when it is a completely syntactic notion that derives just by the expression of the property of the object corresponding to the formula irreducible in the topos so basically it means that every j covering sieve on the formula is trivial so you see this is a completely syntactic thing but ah sorry I forgot the op and so you see here you can really switch from the syntactic thing to the syntac and of course it works in this way so here you have formula and on the other hand you have the model presented by this formula and and conversely and this is a categorical equivalence so anyway you can pretend this could be semantic and this is important because you see you can identify finitely presentable models just by using the semantic definition usually this is what one does one doesn't necessarily care about finding the formula but for our purposes it's important to know that there are such formulas because for making certain computations it is useful so now we consider portions of pre-shift type so, portions of theories of pre-shift type this is a natural something to consider because as we have remarked as any as any glotending topos is the sum topos of sum pre-shift topos so any geometry theory is a portion of sum theory of pre-shift type so we want we often to be able to obtain classic pre-topos of these portions by starting from the representation the double representation that we have for the theory of pre-shift type so we start from this and then what do we do? so we know by the theory that we proved above that if I have a quotient t prime t prime quotient t then it means that I have a sub topos of the classifying topos content but now I move here and I recall that sub topos is of such a topos are just the localizations of these so it means that I have a glotending topology that I would like to be able to describe to describe explicitly in terms of t prime and t basically I mean talking about t prime is the same thing as talking about j but you see that it is not completely clear how to go from one to the other because you see here the formulas are so imagine if you have a discipline like that then you add to t in order to form a t prime how can you find the glotending topology j starting from this you even in the following way you suppose that these axios have a particular form because after all this assures you that there should be a way of presenting t prime in this way since all the sequence that come from j will have a particular form that will involve these irreducible formulas necessarily because you see we are working here and we are precisely working on the opposite of that but the opposite of that is precisely that and maybe we can just write like that emphasize this point expressible in terms of irreducible formulas but this is a bit a bit strange because why should this be the case well, the reason is that you can cover every formula in the classifying topos of the fluid t which is appreciate type you can cover it by irreducible formulas this is the logical translation of the fact that you can cover every every shift in every object of the classifying topos with things that come from the side so what does it mean concretely, but it means that I can cover in this way so this is my geometric formula it means that there exists a jt common in sieve which is generated by formulas that are irreducible so I will have my cover means of course that this and this the disjunction of all this and this gives me the key because in some sense you see, thanks to this decomposition what I can suppose is that I can suppose this to be irreducible because you see we are working inside the fluid t anyway because t is a quotient and I can suppose that my sequence is something of the form because here of course I can always add that so I can suppose that I can cover this formula here by irreducible but then this formula I can send it to this formula so it will give a family of irreducible that go to my formula so I can suppose that I have a situation like that where all these things are arrows from an irreducible formula to our formula which also is irreducible and this is the way to make the translation to calculate j because you see we can exploit precisely this formula and so I mean concretely it as you see there I adjust a sieve basically in in the category c t here and by using that duality this gives me a sieve on the opposite of finally presentable models of the theory so I have got a sieve starting from each axiom and then so this will be so you see also in this case it is not straightforward you cannot do things directly you have to pass through this sort of the composition by irreducible formulas and I want to remark that it is by no means clear even if you take a particular theory of pre-shift type that you should have this way of the composing you see you don't see magic in the sense that you don't even in particular cases these are not trivial things at all and it's full of these situations toposphere is full of these situations so I mean Grotendik was really right in thinking that the notion of topos has an immense potential and in particular the notion of classifying topos adds a lot to it because the logic is of Grotendik's toposis in fact even small changes that you can make the level of the signature of a theory can have a huge impact the level of the corresponding toposis so in some sense toposis are very sensitive to logic and so I mean we shall see in some examples after a break and then I will give more examples of bridges and more sophisticated nature to convince you of the power of this general methodology and of the fact that the toposis can indeed as Grotendik was claiming and indeed after significant places ok so see you later


This episode of the podcast is supported by Audible. You can download and listen to the world's best storytelling. I use it all the time to inform work. You can listen to audiobooks, original series, and more on their free app. To get your free 30-day subscription, which includes a free book, click on the link in our show notes and enjoy. Hey, folks, welcome to the podcast. Today I had a great lady called Sue Uniman come in and speak to me on the podcast. She's currently Chief Transformation Officer at MediaCon and she's author of a bunch of really cool books, the latest one being The Glass Wall, and she's currently writing another one. Not sure what the title is, but it's on diversity. And so we had a great conversation. We looked at whether the current initiatives on diversity are working, how they're measured, and what we can do to make them work better. Really cool conversation. Hope you enjoy it. Hey, it's Lewis. Welcome to the podcast. Enjoy our conversations anytime, anywhere. Cool, we're live. Sue, thanks for joining me. Well, thank you for having me. Pleasure, pleasure. All the way from North West London. Yeah. All the way. All the way. Come all the way from Charlton Hill. Nice. So I know you've written some interesting books and all that stuff and I wanted to talk really for the chunk of the podcast about diversity and where we're at, what's working, what's not, what we can do and stuff. But before we dive in, what is your background? My day job is I'm Chief Transformation Officer at MediaCon, which is the biggest media planning and buying agency. Biggest and best, I say. Biggest and best. Of course, Media Planning and Buying Agency in the UK. So we have clients like Direct Line Group, Tesco, like Sky, Cancer Research, Universal, Theatrical Movies. So a big range of clients for all different types, actually, NCS. And I've been there for a ridiculously long amount of time. So I joined a tiny company called the Media Business, which was a buying shop in 1990. So it would be 30 years. Wow. Next summer, obviously I was a child. Of course. I joined, obviously. Oh, yeah. Straight from uni. Well, I believe, you know, still at primary school, I think it must have been, surely, surely. No, I wasn't, I'd been around, actually. But the company just grew and grew and grew and then we were acquired by a company called MediaCon and we've now grown. So when I joined, we built about 44 million pounds worth of billings of buying clients money and now we're 1.9 billion in the UK. So it's a lot of organic growth and it's a global network. So I've stayed in the same place for a very long time. Must have changed. But it's changed enormously. The jobs sort of technically changed enormously. I mean, our role is to grow our clients' business and that was true in 1990 and it's true in 2019. And our role within that is to really understand people and consumers and understand how to make them kind of all in love with clients' brands and that hasn't changed because people hasn't changed. But the techniques that we use, obviously, are so much more complicated and diverse and include creating content and search as well as placing advertising. So the role is to make sure that MediaCon in the UK and also our clients are ahead of all of the changes and transformations that they need to be. Cool. And have you always done transformation? No, I took that title in 2017. Before that, I was strategy and planning. But probably my thing was always about transformation really anyway. So we now have, Jeff is our very good Chief Strategy Officer in the UK and I'm Chief Transformation Officer. So we work very closely together. Cool. How did you get into it all? Oh, that's a good question. I was going to do law. So I graduated with a history degree. I had a place to do a law conversion course at the Inner Temple. And I had a year off in between. I got bit bored and I got bored. I was making cakes at a cafe in Oxford called Georgina's. Very good at making cakes, actually. Nice. Is it still around now? Georgina's is still there, actually. And when I left, they did ask me to make a stock for them and they put them in the freezer, but I don't think they can still have some of my cakes. Amazing. Are you still baking? I still bake. We need to see you on Great British Break-Off or something like that. Well, yeah, maybe. Don't know if I can stand the stress of the tent. But I just got bored doing that and I wanted to earn a bit of money and so I got a job in advertising. And then with the first pay rise that they gave me kind of six months after I joined, I could afford to leave home. And if I'd done the law conversion course, I would have had to stay living at home probably for another two or three years. And just at that age, it just felt like a no-brainer. You're ready to? Yeah. So I absolutely just fell into advertising. And it was a very different industry. It was very madmen like when I joined as well. We've seen real disruption of the industry by the media or independents, which is where I joined in 1990. And now I have probably one of the best jobs out there. Nice. That's awesome. But I could have been a judge by now, probably. So you know. More fun? I don't know. You must have had a really fun and great career doing what you're doing. Well, yes, I love what I'm doing. But I think, you know what? It's not any way. I think the job. I think how much you enjoy your job is to do with the culture of the people that you work with and the culture of the company. And my experience has been that a lot of people ask for advice about what careers they should be going into when they think a lot about their choices. And my view is that your work-life balance, your job satisfaction completely depends on the culture of the company you're at. And it might even be in some companies, the team. Yeah, very true. That you're within that company. And I don't know if, you know, because it's more your area of expertise. But you kind of don't know that till you get there. So businesses can talk all they like about their culture and the fruit and sweets all day long. But it's actually about how kind people are to each other and how much they help each other. And if it's a sort of culture where you get ahead by pushing down everyone else. For me, that was not a good culture to be in. That was more of the experience in my first advertising agencies. And when I joined the media business in our media comm, the culture is about helping each other to succeed. And that actually is what makes the job fun. It's great. You never know until you join. The funny thing with interviewing is it's really like speed dating. And as you end up, so you meet, I don't know, X number of people for an hour. They make a judgment on you. You make a judgment on them.  I mean, when you're deciding to get married, you don't decide after one hour, right? You go out with them, but you don't want to get married, you can, et cetera, et cetera. So it's a funny thing. Yeah, it's suboptimal as a process, isn't it? Yeah, 100%. I mean, you can use psychometrics and all of these And people do, but I'm not sure any of that makes... It gives you a better chance of making more... But you can't psychometric the company you're joining. So that works perhaps on the candidates, but yeah, you don't get to go, can I psychometric the people that I'm going to be working with, please? No, you don't get the opportunity. And it's not until things go wrong or you go through tough moments, when you're really in the trenches with someone that they're real kind of what they're about comes out. And more and more, when I meet people, senior execs that are thinking about leaving or you kind of delve into what their motivations are and always people-related, if someone's changed or they're not going on with their team, those kinds of things. That's what people say, people leave managers, they don't leave. Yeah, absolutely, yeah. Over and over again. It's funny, like a lot of people think people move for more money, and the money's much further down the list than people think. It's always the people aspect and the culture and stuff like that. So as well as me being, having been at MidiCom for a long time, I've probably got about 25, 30 colleagues that I've worked with for more than 20 years. So there's a lot of people that are still hanging around, which again is a sign of, you know. Yeah, there's a lot about the place, definitely. How did your book and your interest in diversity and stuff come about? Well, it's connected really. So I'd written a previous book, which was about marketing called Tell the Truth Honest is Your Most Powerful Marketing Tool, which came out in 2012. And in about, must've been about 2014, 15, I started thinking about writing another book. And originally I was gonna write a book that was a follow up to the first one to tell the truth. So I went to my then Amir boss, now my global CEO, who's a man called Nick Lawson, who I've worked with for 29 of those 30 years that I'm coming up to. And I said to him, first book was published by an American publisher. I wanted to do a follow up about our clients. So I said, you know, would MediCom consider self-publishing that for me rather than taking it out? Cause it's gonna be more of a PR piece than a critique or a scope is. And he said, just to my surprise, he said, Nick said, he said, yeah, he said, actually we would, he said, but I've been thinking about you and that's not the book you should write. You should write a book about women and work. And when he said it, my initial reaction was, well, I don't know, Shara Sandberg's just published Lean In. I like bits of Lean In, but it's very much a book for extroverts and I am very much an introvert. I mean, I do my best, but I'm, you know, by nature an introvert. And if I'd read that when I was in my early 20s, I honestly would have just gone back to bed and, you know, called the covers up. It's like, it's so Lean In, put your hand up, do this, do that. So I thought, well, you know, I don't agree with all the advice in it. And it's also quite American.  Well, you know, who's got that contact list? So I thought about that. And then I looked at MediaCom at the time. So my UK business at the time, we had quite a small ex-co, senior ex-co, of which I was one. And four out of the five client-facing people on the ex-co were women. And three out of those four were working part-time because of having kids, including me.  People are always pitching for our clients because we've got lots of clients. But also, it's 24-7 business. I mean, if we have told a client that a spot is definitely gonna go out and Britain's got talent and it doesn't go out for whatever reason, no client goes, I'll tell you what, I'll wait till 9, 9.30 Monday morning before, it's like, we're on it the whole time. Christmas day, boxing days, someone's, you know. So if I think if you'd said to most organizations, so what we'll do in that kind of businesses we'll have four of the five top people will be women three out of the four of them be working part-time, it's fine, isn't it? Most businesses would go, no. Now it had happened at MediaCom organically. Everybody had been promoted from within. Everybody had just worked their way through up through the ranks. And I just looked at our competition and then I sort of just kind of looked up, looked up, looked around. And about the power of it. Yeah, and looked at everyone else and looked at some media owners, the media owners that we work with and that kind of senior level of women wasn't anywhere.   It is sort of isn't possible that given the number of women that there are in the population that all of the talented women had happened to rock up 124 Theobalds Road. I mean, I'd like to think so, I'd like to think we're very good but it's kind of statistically not possible. So I went to my co-author, I'm going to wave the book, regardless of Catherine Jacob who is one of the very few women CEOs of media owners. So there are a tiny handful of women CEOs that media owners, she runs Pearl and Dean, the cinema company. And I said, what do you think's going on? And she said, I don't know what's going on. Why is media can't be different for everyone else? So we set out to find out. So we went, just started interviewing people. We've got Quant Search in the book as well. Awesome. And we ended up with The Glass Wall. Nice, nice. And how long did it take you to compile everything right here and? Well, the longest part of the process was finding a publisher. So I was very aware that you couldn't self publish. But I wanted to work with a publisher to edit us and kind of give us discipline and it took us a while to find profile. And so probably during the year that we were looking for profile, we were doing the interviewing and kind of forming our point of view and our perspective.  So about two years in total. Amazing. And this was all UK focused kind of interviews? No, mostly UK. But we have stories in the book from around the world, America, kind of Australia. And the research is the UK, the quant research is UK, US and Russia. So we did working populations of those three countries to make some comparisons. Nice. So are the current diversity initiatives working? I mean, the gender pay gap went back year on year. So from the first year to the second year, it actually went backwards overall. And what's happened since the book was published? So what's happened? Just to remind of it, so it was published in... 2016 is an enormous amount of raised profile for diversity and inclusiveness. An enormous amount of initiatives. But actually, I can announce that we've just been commissioned to write a follow-up. Amazing, amazing. With Bloomsbury Publishing, which is very exciting. Congratulations. Thank you, very excited. We're now writing it. So everything's... So your material is... Everything's material. Absolutely. It's about what needs to happen next because I don't... Empirically, if things are changing, they're changing very, very, very slowly. And I think in some examples, they are actually moving backwards. There are trends. So although everybody is thinking and talking about diversity and inclusiveness much more, there are mitigating trends going on in the work environment that are actually not helping with senior women being promoted. And I think there's a lot as well of emphasis on this is the job of HR, whereas in any good culture, it's the job of everybody in management. Before I started writing the book, if someone said to me, MediaCon has been very successful. It was a tiny company when you joined. We've had exponential growth since then. Why is that? And my answer would have been diversity, the diversity of senior management. And not only diverse in terms of how we look and where we're from kind of of origin, originally, because we're, you know, and indeed, LGBT, all of that kind of thing, but also diversity of thinking. And one of the things, one of the things that we talk about, people obsess too much about cultural fit. And what happens if you are an employer and you're looking for someone to fit your culture, is that you get the same culture of putting yourself over and over again. It limits diversity in the hiring process for sure. And we talk instead about Avengers Assemble. So the idea that what you want in a great team is you want who are different, but who can work together, you do not want a room full of incredible hulks, but an incredible Hulk and an Iron Man and a Scarlet, which great. And that's what had happened at Media Commons. I think that's why it was successful. Without trying. So it wasn't contrived, it was... It was organic. But I think when you say without trying, what we were trying to do was win. And so because we were so competitive winning pitches and things, because we were so competitive, we said, let's employ the people that were talented. And one of the first things that I did, first press interviews we go for the book for the Glasswall, was with Joe Good on Radio London, who's brilliant. And she had an email flooded in as a question. And she said, the email said, look, you've said, Sue and Catherine, you've said that there's a Glasswall for women at work. And I can explain a bit about what that is, if you like. But she said, wouldn't you agree that it's a concrete wall for black women at work? And she said, did you know in this email? I said, did you know there's only one media agency run by a black woman? And I said, yes, I do, because that's my, she was in my chair. That's one of my bosses, Karen. And I sort of thought about it.  We proposed to her because she's really good at her job. So does that mean that if she'd worked elsewhere, or if I'd worked elsewhere, we wouldn't have got promoted despite the fact that we were good at our job? Because the thing about gender diversity, and there's a lot of intersectionality now, which makes some people lean back because they feel it's too complicated to deal with. But the thing about gender overall, encompassing women of color, and women who are lesbian and disabilities, et cetera, et cetera, is that women are not a minority. And yet we talk about them in the workplaces, though they are. And yeah, nope, there's about 30 million of them in the UK. And it just beggars belief statistically, given that women have been, had a full share in the workforce for 60 years, that none of them have organically risen up to the top anywhere else. And so what you're saying to sum up, the current initiatives that people and firms are doing just start working. And then what you're seeing now is... Well, they're working a bit. A little bit, but nothing outstanding. And then I see it, and I don't know if you see it, but I see now a bit of a backlash towards these diversity initiatives. A lot of the time white men who feel that they've been marginalized, they can't get the promotion, they're not getting on the short lists and stuff. Do you see, are you seeing much of that? Yeah, so I think there are two, I think if you're a straight white man in the workplace at the moment, there's two sorts of reactions that are around. One is largely the good guys who are going, I really want to do something to help. But let me tell you, the risk of me saying or doing the wrong thing is so high now, it's career destroying. I'm just gonna sit here quietly and wish everyone well, but I'll shut up, shall I? So that's one thing, and that's not helpful. And then the other thing, particularly bearing in mind that it is still white men who hold the roles who are powerful, they have the power, is the men that are kind of upset and worried and frightened, who are feeling like they're not wanted, who are having a very bad day on International Women's Day, which is now massively celebrated everywhere, because they're feeling like nobody wants them, who if they miss out to a role or a promotion to a woman, you know, obviously I have no idea what's going on in every instance, but it may be preferable to think that you've missed out because you're a man, because you weren't good enough. I don't know, maybe that level, but then the more important level is like young people, right? Like grads or school leavers, so just people in society. And so the big danger you find in this backlash, it's at all levels, it's people that, I know if I look at my social circle, maybe I'm too optimistic about it, there's no sexism or racism or homophobia, people have friends from everywhere and we don't really care, you know? But it obviously gets into society somewhere. And I think the danger with some of these initiatives, which haven't really worked so well, is that you don't really want it getting in at the early age. You want people to feel, because the whole point of this is it's about fairness, right? So equality means... It's about inclusion. The inclusion initiative shouldn't leave out straight white men. Yeah, it should be inclusive of everyone. It should be really clear.  Well, that's just not helpful. And what do people think is gonna be the reaction to that? And yeah, no, certainly, I know a couple of women who've got teenage sons. And one of whom in particular said to me, he came home from International Women's Day at school and said, that's the worst day I've ever spent. He said, nobody wants people like me. And I've had another story about a very... This is a public school young man who was doing a kind of law degree who was at the point of tears because he thought he had no prospects, which is, again, not what happens if you talk to anyone who works in the legal freshen as a woman, that's not the picture. And so, and look, I read something today. This month is an anniversary of the first college of surgeons for women in America. So it opened up in the 18-somethings. I can't remember the exact date. And the man who ran it, because it was a man, naturally, said, well, there's around 40,000 surgeons operating in America today. 20,000 of them have got to make room for women, right? Okay. Is that what happened? No. How many surgeons are there operating in America today? No idea. More than 40,000, right? So it's not a zero-sum game. It's a growth business. And if you are in business, you will grow if you take a proper approach to diversity, right? So it's not, well, there's only room for so many people on this board. It's, let's grow the board. Let's grow the business. Let's add diversity to it. I mean, the interesting statistics, I think, and there must be some new ones about to come out are the footsie board figures because they've been celebrating the growth of the number of women as a proportion on those boards, but most of those women are non-executive directors. So I think it was 30% was the last figure, which was last year on the footsie 100. Do you know what the, and that was up from 2015 when we wrote the book. It was 26%, so that's grown. 2015, the number of executive women on, so actually working for the company on the footsie 100 was just 2%. Guess how much many there were last year of executive women on the footsie 100? Probably very similar. It was 2%. It had popped up to 3%, I believe, during 2016 and then rattled back down again. So the interesting thing I think here is then you've got, so you've got two things. So clearly whatever we've been trying to do recently hasn't worked so well. Well, it's working slowly. It's slowly. And in some areas it's not working. It's sort of, it's alienating some people. And it's alienating some, and that's always a curious thing. Like a lot of people try and justify diversity by making a business case for it. Really, it's like, it's society's better if society's fairer. That's definitely true, yeah. I've always found it interesting why people are trying to make a business case for it rather than just a case for a better society. So that leads you on, and I'm interested to talk about the measurement of diversity because it's quite one-dimensional, which is interesting. But to start with, if it's not working, what should we be doing differently? I think it's really simple. I think it's about, it's a cultural issue. It's about inclusiveness. It's about belonging. And we're writing the book at the moment. So I've got 75,000 words to write by the 31st of March. They're not all written yet. So with my co-authors, Catherine, and also Mark Edwards, because we thought, because this book is aimed at men as well, definitely, we're gonna have a man join us as an author. And it's, we're still working through our arguments, but I think it might just be really simple. It's about ensuring that it's everybody's responsibility. So outsourcing it to a head of HR. I think that's the schoolboy era. A lot of firms do outsource it to people, even outsource it to headhunters. Oh, you get blamed. So not you personally, but I will get told the headhunters couldn't find anybody. So I get asked, and this is, and this kind of goes against my own values. And I'm into equality, inclusiveness, et cetera. When I get asked specifically to find a certain type of person, it goes against what I believe. Because you wanna find the best person for the job. No, not the best person. All I care about is that the individual and the company match. And it works well. And they stay for 30 years and they do a great job, right? Don't really care. But is anything ever gonna change if nobody takes, if nobody goes looking for? So I think personally, for my own view, the measurement, the way that diversity is measured in the public domain is two one dimensional. It's kind of like, you know, people measure their health on, you can't measure your health on calories and weight. It doesn't tell you anything about how healthy you are. So a lot of the time in diversity, it's measured numbers and pay. It doesn't really tell you anything about what's going on in society. And hence, we haven't really seen a huge amount change. And you see a little bit of some people in society being alienated and, which is not a good thing for society either. So for me, really the big thing is stigma. So if you look at, you know, if you look at who looks after the kids, for example, I'd say, I don't know what their actual stats are, but let's say it's 95% of the women in a relationship look after the kids. You mentioned it yourself. You didn't mention any guys, but you said three of your, including you, of your leadership team were part-time. I'm assuming that three were women. So we do have some men now, but at the time it was only women. Yeah, and even now it's women.  Still.  I'm a stay at home dad. You can imagine the reaction. Paternity leave and paternity pay is not equal either. No, and men are not taking it. They don't take it because of the stigma. I mean, I had a friend, two friends, or one friend of mine who was able to take six months, six months paternity full pay. So the economics worked out for him and his wife. And he said, look on people's faces. And in fact, his boss said, really? Are you sure you want to take some, you know, you want to take that long? It might affect your progression opportunities, your career, you know, all of those types of things. So for me, if you really want to kind of really get down into it and make it fairer, because for me it's about a quality of opportunity rather than a quality of outcome. Quality of opportunity makes for a really fair, open society. And if I have the opportunity to stay at home and look after my kids if I want to, and my wife has the opportunity to go and pursue a full-time career if she wants to, then I think we'll start to get to a better place. Okay, so what does that mean for, and I saw the reason that people make business arguments is because it's within the remit of business to change that. Society feels like a very big nut to crack. Do you think it's a... So interestingly, I read in our trade press today that the government is tendering for a campaign about getting rid of the gender pay gap. So it's going to be some sort of creative advertising campaign. So I was just thinking about it. So I think you're almost thinking you need behavior change or cultural change for the whole of the country. Definitely, yeah, because I think at the moment it feels like contrival. Like, you know, when someone asks me, okay, so I want, so when I submit a long list, and sometimes companies in the UK ask me to sign up to this. So if I don't produce X number... A 50-50 list. 50, it's even split also with BAME or FIMA, whatever it might be. The very fact that someone's asking me to contrive my list doesn't really make me feel comfortable. And also I can't think why it's, it's not a fair way to go about hiring. And so I think there's better things you can do to get the same outcome. And the outcome should be a fair society. Quality of opportunity. You know, it's very different in Scandinavia. You work this. So everyone always says, if you want a husband who's going to support you in your career, marry someone Swedish. So maybe it's cultural. Maybe it's upbringing. I think there is a cultural. There's a lot. I think my point is there's so many things that go into it. And it's not so one-dimensional. It's like health and fitness. I might be like considered overweight on the BMI scale. Actually, you know, it's all muscle. I'm super fit. My cardio is amazing and my heart rate's great. There's just a lot of things that go into it. And so I think with measuring diversity, it needs to be multi-layered. And then once you start really understanding what's going on in society, then you can make society fairer and better. The thing with the quality of outcome, which the conversations tend to end up leaning to is you never achieve a quality of outcome ever. It will never ever be achieved because people have different strengths and traits. And, you know, we start on the 100 meter line and you're quicker than me. You're going to beat me. Genetics, training, whatever it might be. Well, I mean, certainly something that somebody said to me, he's like a non-executator of a number of boards. And he said he was interviewing for a CEO role for one of them. And it wasn't a question of a 50-50 split list. The shortlist was through one in one man. But he noticed as they went through the interviews that all the, for the opening question, which is, what have you done that you're proud of? Nice easy opening question in the last two, three years. You know, everyone, well, everyone should have an answer for that one. He said, the women were going, we did this, we did that. And the man was going, I did this, I did that. And he realized, and it's only in the conversation with the rest of the panel afterwards, that he had therefore discounted the woman's agency in it because she'd said we. And it was the other women on the panel who went, no, no, no, no, that's just how women talk. And you almost kind of, and he said, he wanted to ring them up and go, you need to say I.  Yeah, yeah, no, you're right, you're right. And those sorts of things. You see, I think you can as a, in your kind of day job, that's the kind of thing you can. We can coach people. Coach and help people. And we do, yeah. I mean, so that's why I think, you know, you've got to go right, even to, you know, my kids are at school, they're super young and I'm trying to teach them these kind of things where I had to communicate effectively, how to learn, how to think. It's a real, that's a real glass wall thing though. So the reason we called it the glass wall and not the glass ceiling as far as gender was concerned was because the glass ceiling implies it happens towards the end of your career, when you're like reaching the top. Whereas the glass wall can happen all of the time. It can be your first day in a new job, it can be a change of boss in your current job and things have changed. And it's a communication barrier. It's a, you think you're speaking the same language that you're, but you're not. And one of the biggest ones, as far as gender is concerned, and I don't know, obviously you're little girls, but I think this seems so strong in women versus men and everything's a spectrum, right? But it's the showing off thing.   It's like, it's not all your influence anymore. It's the big soup of culture. And I mean, to this day I work with women who would do anything for their business. So they will work weekends, they will say, no, no, no, don't give me a pay rise, give it to the rest of the team. They will, you know, support the company. And the only thing they won't do is show off about their work. And when you say that to them, they get quite upset because in terms of fairness, women seem to have this deep innate thing of, but surely you should notice if I've done good work. And the answer is, is your boss is busy. And if he's a really good boss, or she's a really good boss, then you're right, she will notice. But if she's doing a million things and in today's economic climate, we're all doing a million things, then the thing that sticks in your head is that person, and largely often it's traditionally a man who's going, yeah, no, I solved that huge problem. Remember that huge problem, I solved that, whereas women are kind of just going around solving problems, but not shouting about it. Yeah, no, it's probably, yeah, probably true. But then the other thing is, and you see it in my girls, but it's important to develop people's strengths. A lot of people focus on these weaknesses. I so agree with this. Should be shouting, or just, you know, make sure your strengths are amazing. Yeah, I totally agree. Practical strengths. So much training is improve your areas of weakness. I've been on so much training to improve my areas of weakness. And I realized at a certain point that they weren't improving at all. All that was happening was that the energy that I could have put into my areas of strength, which are many, I have to say, was being wasted on trying to sort out areas of weakness, which other people had strengths in. And again, it's that hideous sort of idea that everybody's got to be the same rather than complimenting each other instead of competing. It makes no sense, does it? No, absolutely. And in a good team, you have different traits and strengths and so forth. But people like to control things and they like people that are like them. And I understand that as well. So I do understand how, you know, if someone were to go to you, and obviously it's your business, but if someone was to go to someone and go, Pete, we're gonna promote you, but you've got to find a number two who's as good as you and then we'll promote you. And then Pete is naturally gonna think, well, I know I'm really good at my job, right? Because they're promoting me. So if I find someone who's exactly like me, it's just brilliant, isn't it? Because so there is that part of human nature as well. And to say to Pete, right, the thing you need to, the very thing you need to do is employ somebody who's the opposite of you. It does, it's not very human nature in a way. No, people like people like themselves. You can't get away from it. There's a great book by Daniel Kyneman called Thinking Fast and Slow, which is really good. Very good, very long. Very long, complicated, great to say that you've read it, even if you haven't, I have. But anyway, the point is that we're all, we're all buyers, right? Yes, it's all buyers. We can't help it with human. And that's how the world works. Yes, it's the, I like his analogy of, we think we're the Oval Office, but actually we're the Press Office. It's kind of like, not that actually the Oval Office meant what it does now, what it, when he wrote it, but. Yeah, no, it's true, it's true. We're jumping to immediate decisions. Yeah. The other interesting thing I see also is, and again, I'm gonna sort of go back to stigma. Because I think it's a really... Stigma's an interesting point. Yeah, a really, really key thing. And you're talking about it with regard to men. Both. So I'll give you some examples. Some men on paternity and looking after their kids for sure. I think if we, because there's an awful lot of men that wants to look after their kids and be a stay-at-home dad. And there's a big stigma, let's be honest, in society towards that. And it doesn't happen so often. They do it, brilliant. Are you watching Motherland? No.  Really? At least it's so funny. But one of the dads is a stay-at-home dad. Right, okay, right. And they do how he fits in and doesn't fit into the other mothers very well. It's very funny. Oh, what's that? And everybody that I know that's watched it goes, they've definitely based it on people I know. I've got to watch that. I've got to watch that. The few, because there's not many, the few stay-at-home dads I know. And we're talking about strengths. They've met a partner who didn't want to stay at home in a car for the kids. And they are outstandingly doing well in their career. And said that the team has enabled it. Amazing team enabled it. There are a few of those around, much more than probably for our parents' generation. For sure, yeah, yeah. But it's still, I don't know. And so, and I'd like to see that more. There's also a lot of stigma towards women, from other women. It's a client of mine. She's an HR director. She has, I think she was two or three kids and she was dropping, she was just finishing maternity leave, dropping her youngest kid at school and the women who were at the gate. There weren't any men. Said, oh, do you want to come for coffee next week? And she said, oh, no, I'm going back to work.  She's like, actually, I want to work. And so I think it works both ways. Like a woman should, or man, should be able to go and work if they want. They should be able to, if economics and all this stuff works for them, be able to stay at home. Because in a lot of families, both people need to work. Let's be honest. In the real world, yeah. Like in the real world, you can't just be a stay-at-home dad or a stay-at-home mom. So it's all dependent on the circumstances that you're in. But do you know what the problem with all of this is then? And it's probably going to be a big theme of the book, is it's about kindness. So people do not assume the best intentions of each other, which is a lot of where the, I'm trying to say the wrong thing comes. Well, if you assume the best intentions, if you have the best intentions, we should be able to forgive each other for occasionally getting things wrong, because we all get things wrong. But equally, amongst that friendship group, and I was at the, my kid's school, I was one of the few working mothers in the class. So I understand that, because also you miss out on some of the network stuff that actually you need as a working parent anyway. You know, I had, I made some very, very good friends and I lent on my friends who weren't working very heavily, heavily more than I had any right to and they were very kind. But there were other mothers who were a bit kind of, yeah, a bit dismissive or even perhaps envious. But that's how it exhibited itself. And the other, if people were more actively kind, I mean, you know who your friends are, right? But the other aspect of that is what happens.  And the five, 10 years when you're needed in a different way from kind of like when they're three to when they're 13, it goes so fast as a mother and so slowly kind of, you know, if you like for the kid, but career-wise that's a long time out of the workplace. And I have also, now that my kids are grown, I've seen that as well. And I've seen actually highly educated, very ambitious women when they had their careers who then stopped their careers, then go, what do I do now? And actually if they had to work, they would be on the checkout, you know, little or whatever, getting on with it, but not having to work, not being needed for school runs.  Yeah, absolutely. And I've seen that difficulty as well. So there's an awful lot at play there. Yeah, and just like on the diversity metrics, I think it's important to make sure it doesn't hurt us because ultimately you end up isolating and tallying differences in society. And really, I mean, certainly now you have Brexit and the country seems so divided and stuff. You just need to be careful it doesn't prevent us from realising how much we all have in common. Yeah, I think that's very true. Which is kind of with the priceless thing. My big thing about culture at work as well and in society in general is if we, you know, I think we all agree that it's not very nice for people to be made to feel other or made to feel different or embarrassed or, you know, excluded, but we don't all do something about it. We have all been a bystander in our lives. And if we all today, right now, from this podcast, all agreed, I will never be a bystander again. I will speak up for other people. Then we would get that change that you're talking about. And that's within all our power, actually. Definitely. What a beautiful place to end. Thank you very much for coming in. Please let me know when the book is coming out. Do you have a website that we can... We have not created a website for the next book. There was a Glasswall website, but there are... Glasswall is on Instagram. OK. Oh, cool. And I am on Twitter at Suyou. Perfect. So I tweet more than I Instagram post. Tweet more than you gram. Yes, I tweet more than I gram. But at Suyou, I am for updates and news about the book. Awesome. Thank you so much. Really nice to meet you. Good to speak to you. Thank you. Hey, folks, thanks for listening. Don't forget to subscribe in all the usual places.


I was trying to tell Kiki like, bro, I probably wouldn't have been a hoe If I wouldn't have listened to y'all music as a child because y'all Y'all told me how to gaslight and tell this woman Everything will be fine if you just stay down. That's a lie.  Here we go.  Here go another nigga with some ice on his chain If if I could change everything all over again all the walking them bitches looking like silo green I mean not silo, uh Jermaine the pre at the super bowl.  You gonna remember me But I was forgettable. Let me just say that that's hard That's hard But it's real and and it's good that you take notice to how you know who you are your self evaluation is real You know self awareness. That's a real thing And I think that's hard that you look back reassess and say, you know if I did this Because now when you in those situations, you know how to conduct and what you need to do to be successful I'm starting to know what cowboy has on him on the ass ice that no sir Nigam not want to be in the studio with me, but hey Man, let me ask you this man. Um, uh, we lost a real one down there. Uh, big poke man um the sense say like like When you've seen that because it happened on the internet and I know it messed with kiki bad because that was his boy That was a right-hand man. Like they always was together on Videos doing a thing, you know, I'm saying their era, you know as you see and all like, what did you what did you think when you seen that happen?  Like I'm a real I'm a dj.   Yeah, I seen it. I seen it. I told him to his face I told kiki. I said man. Y'all was the best gas lighters Wow, and he was like, what do you mean shows?  You gotta understand a lot of a lot of people A lot of people to be real with you they they tend to forget that they'll say man zero He was the first one singing like that but really to me with fat pat Man, how I'm chill with my bra I was trying to kiki like bro, I probably wouldn't have been a hoe If I wouldn't have listened to y'all music as a child because y'all Y'all told me how to gas light and tell this woman Everything will be fine if you just stay down. That's a lie. That's a That's a lie But I'm good at it And it's all it's all the niggas fault I heard some kiki. I say man. I looked in his eyes and said, you man.  I'm being real. I thought it was a black dude. I heard him on the radio when I first heard him I met him. We've hung out a few times Like when you see him and the way he is with the culture down in houston and what he's done What do you think for us when he come down to pow wow, you know in his his movement I love pow wow and I feel like I know I said what I said about how Everybody shouldn't be accepted, but I feel like pow wow one of them people that's of hip hop I didn't think you about you say that for sure. So when I say that I'm speaking on people that's not of hip hop That's just benefiting out of it. I think pow wow was of hip hop. He should be and he is accepted because we know he's of You you know, I'm saying niggas talking about I'm on that five nine south league anybody that nobody five nine south league No, you shouldn't be on five nine south league Since pow wow, baby What's it know about me? I'm on that five nine south league Because he's someone he's too close to have a star my cousin stay over there right by him. He's too close to have a star He's too close to So when he said that I'm like he he's just talking, you know and I I'm a big fan of um one of my favorite songs is um Just the other day with him in a cameo, right? I'm not the type that likes to think about the time. I was broke and reminisced So everybody thought my rhyme was a joke and cameo the bees too when I'm balling balling balling balling My neck is crawling. I would rest is calling.  Oh, yeah.  Wow respecting me just like kiki did um slim did like I'm I'm just You know, it took some of the legends a while But I just be happy that it came about because I ain't got no negative No envy for these niggas, you know at early on I might have had a I might have felt the way about like a row or something But when we finally met and I finally went to row house It came down we talked and I realized like man Man, I'm niggas them niggas wouldn't hate no me. They had no problem with me Them niggas was just in a bag like I'm in right now Yeah, we on boss talk one-on-one one-on-one. Yeah, we gonna talk


Hi everyone, Joe for jazby's case rakes comm happy new year coming at you with 2020 panini impeccable football three box picker team number 21 Thanks to all of these lovely people here for getting into the action That Jimmy Brant with I think double last-bought mojo with the Lions and the Seahawks cat and bird team mojo At the end and we had a little number block randomizer, which is in a separate video. Did I upload that video? Stand by yes, I did so if you're looking for that is uploaded right now And let's see what we got in this bad boy right here quick little three box break We'll take us to the top of the hour and then Sean Jaspy will take over He'll he'll break for at least a few hours But he'll go he'll go for five seven eight hours Things keep filling so keep filling it up folks jazby's case of breaks comm There's Charles Woodson. We were just talking about him Hall of Fame finalists in first year of eligibility First battle Hall of Fame are pretty easily The proudest thing you've done Super Bowl championship with Packers. Yeah, that was a good moment And then maybe also how you can rock and ask God Without losing an ounce of masculinity. I mean that there's that too. There's a true lock For Kurt disser and the Broncos You know There's David Montgomery to 75 for the Bears Bears are a number block team, so that'll be Bears 2 Chicago 2 will be Steve Birch We've got Damien Williams elegance two-color patch and autograph to 25 It's a good question rebel So the ha so on ha the Hall of Fame one can everyone get in the Hall of Fame or a set number of players I Feel like the Hall of Fame is pretty like an NFL Hall of Fame is pretty stingy on how many players get in for summaries I actually don't know how that works Chiefs I go with that one with can't see chiefs No, Ian saying that that Woodson's fashion is too strong for TV It's not like he's wearing like Cam Newton outfit. There's Dalton Keen 72 out of 75 He does look like a gentleman from like Victorian England though There's Dalton Keen to 75 for the Pats. That's gonna be for Karen and her Patriots There's Frank Clark 23 out 25 indelible ink for the Chiefs another one for I gordon He does outdress everyone around that's that's for sure I wish I could pull off an ascot not too many not too many people can I feel like There's Dalvin cook 58 out of 75 nice Dalvin cook He just needs to stay healthy, but he had some pretty incredible games Dan with the Vikings you can play 16 full games Imagine if he could be as healthy as like Derek Henry Be putting up some nice numbers, too And for the Jets la Michael P. Ryan nice dual relic. Is that a piece of the helmet? It looks upside down helmet sticker maybe 15 out of 35 That'll be for the Jets Jets Jets Jets Nick Esposito Next box That's the case hit by the way. We're gonna do that last I did not oh I did see a Deandre Baker's injury they they they took they actually had to drive a Mini ambulance in there to I Look brutal. We got Mark Ingram to 50 Patrick with the Ravens trend center What's going on? Happy new year And Kyle and everybody else and got George Kittle to 75 Niners Ben with the nine hundred the Niners play without Half the squad it seemed like at various parts of the year if that Niners team was healthy if they have a decent quarterback We got a blockchain a redemption card to a Tungo by Loa That redemption goes to Miami Miami is a redemption team Number block team Jared Jared Brinkner with that one now Well, however you feel about these blockchain cards these digital only blockchain cards It's a big name like to Think they actually go for a piece of my mind. All right. There is lawyer Maloy 68 out of 75 have the have the Patriots Have had have they had the most lawyers on their team in recent in recent memory lawyer Maloy Thai law Ben Jarvis Green Ellis the law firm We've got Lance Briggs 45 out of 75 bears bears are a number block team bears five is gonna be for David also. Oh nice Daniel. We can add that to the schedule a little bit later tonight You've got Jonathan high tower the fourth J H IV 79 out of 99 for the Fly Eagles fly Blake with the Eagles Kings you don't want the blockchain card. I don't think the good news is I don't think it replaces a card in here So you're getting the full slate of cards. The blockchain is just an extra. I Think there's Jerry Judy three-color patch and autograph for my rivals the Broncos 65 out of 75 Denver Kurt dissert there you go Kurt Jerry Judy shakes the drop seas He's gonna be really good too. The redemption is Clyde Edwards E. Lair Chiefs that's gonna be for Igor and Casey. I think I'd have a bigger complaint about those blockchain cards If it actually replaced a card in there in this box No, yeah, I mean I Think I like that. I like that. They're Trying something new, you know, so they're not being stagnant about the way they see the hobby But I think it'll take a while before stuff like that. It's gonna really Catch you know, there's Antonio Gandhi golden 10 out of 75 piece of the helmet it looks like and a three-color patch That's a good-looking card for the Washington football team. I'll cost it But yeah, I think I think majority of the people still want the tangible card But there's there's been a bit of a small footprint You know a foothold that the blockchain cards are getting now if those blockchain cards actually turned into real card Then I think I think People would feel differently about that, but maybe that's that's those blockchains the first step towards that I don't know. I have no idea what the long-term plans are, but That's the holy grail right trying to blend the digital world with this tangible world All right last box in the case hit good luck, there's Miles Sanders to 50 I think he was one of the guys among others not happy with the way that Eagles game ended Baker Mayfield to 50 Cleveland Browns. That'll be for Daniel Anderson Browns. No Kevin Sifanski How's Baker gonna do without his head coach who I think is a candidate for coach of the year It's gotta be one of the you know, he's got to be up there He's got to be amongst the top three five quarter Head coaches to win coach of the year, but now they don't have him this week and that's gonna be tough Jared Goff It's Sean Mcgabay gonna do without golf and his thumb Did you see that his thumb was pointing this way and then he popped it back in and then the day after he got surgery He got pins put in his thumb and now they're hoping he's gonna be ready for Saturday Saturday Is there a picture of his his Thumb, I don't know where the doesn't say where the pins are where they put the pin Trying to figure out where where they put the pin. I don't know where they put the pin Let's either him or John Wolfer Rams that'll be oh, that's a number block team. So Rams four We'll get that one Los Angeles Rams four is jms We got the long arm of the law lawyer Maloy 14 out of 75 I guess those toplers want to hit the bell that goes to Karen and her Patriots That's true. His he does live pretty close to us down the street. Maybe we should go over Should I send him a carer package? Maybe some icy hot. Here's kj. Hamler 23 out of uh 25 That goes to denver That'll be for kurt and the broncos You got steve largent Speaking of hall of famers. You're doing a hall of fame finalist thing here. Zach thomas a hall of famer He's in his eighth year of eligibility Two out of 25 steve largent. I think when he entered the hall of fame. I think he had He held a lot of the passing records Big passing words, there's james harrison nice 14 out of 15 Steelers jms jms is a stealers guy There's a super bowl champion james harrison He's pretty good There you go. Nice And the last one here is cd lamb 42 out of 75 looks like a piece of the helmet and his jersey Cowboys jms also has the boys strong finish Joe. All right and the case should calvin johnson be inducted What what ballot is this for is this his first ballot? I feel like there's a wide receiver Backlog isn't there like there's like a bunch of other Guys that probably should get in I think eventually he will be But I don't know if any I don't know if any time soon All right There is brandon iac Nice troi ounce fine fine silver in the nfl shield right there 13 out of 20 That goes to ben hoda with the san francisco 49ers and there you go boys and girls. That's uh 2020 impeccable football three box pick your team number 21 I'm joe for jasky's case breaks.com. I'll see you next time for the next break. Bye


आई, मिसे स्विना सुनिल पत्की, असिस्टन प्रफेसर, दिबाट मेंट तोफ लेक्टानिक्स अंजेनेरिं, लोक क्तरतित कय कात सक्वें? और रिएद्दवाट मेंगन लॏक्ताइ विजी तुछक耶॑शलिक्रु off rota ji sakri lampi tahi bundri laght aata. हम न거। दû मेंट ल्रचा। carajurajam hai cupboard. Now pause the video and think, what is the special feature of single phase induction motor? High starting torque, low starting torque, average starting torque, zero starting torque. So what is the answer? Answer is zero starting torque. That is why we can say that the single phase induction motors are not self-started. So this is the special feature of the single phase induction motor. Single phase induction motors are not self-starting due to pulsating magnetic flux. To create the rotating magnetic flux, two coils are connected having 90-degree phase difference. The phase shift is achieved by resistance, inductor and capacitor. So according to starting methods, these are the types of single phase induction motors, split phase motors. So here the two windings are provided. That winding are generally connected in parallel with each other. And the resistance start motor, one winding has the higher resistance than other. So main winding has the low resistance or we can say the more inductive winding is there. And the starting winding has the high resistance as compared to main winding. So here the phase difference is created. So second is the capacitor start motor. So one capacitor is connected with the starting winding. And the phase difference is created due to capacitor. Third is the permanent split capacitor motor. So here permanently two capacitors are connected in series with the main winding and starting winding. To create the high starting torque, we are going to connect the capacitor. So next is the two-value capacitor motor. So to increase the power factor of the motor, we are going to use the capacitor in this single phase induction motor. And the shaded pole induction motor, the pole is divided into two parts which create the rotating fluxes in the motor. And we can make the single phase induction motor self-started. So these are the types. Let us discuss all these types in next session. You can refer the books, Electrical Engineering by B.L. Thareja, Principles of Electrical Machines by B.K. Mehta and Rohit Mehta. Thank you.