So I want to have a sort of a grab bag of topics in this last lecture. So I've talked about infinity topoi characterization in terms of descent, local classes and universal families and truncation connectivity. So I've noticed that the, I can look at the full subcategory of in truncated infinity group oids. And so these are what are called in group oids or sorry. Yes, these are called in group oids. S less than or equal to zero is equivalent to the one category of sets. S less than or equal to minus one is equivalent to the one category actually poset of propositions. S less than or equal to N is an example of an N plus one category or as I said it's really in plus one comma one category, but I'll use Larry's terminology it's easier. So in this setting and is an N plus one category of all of its mapping spaces are in points. That's the definition. So just as we can look at pre-sheaves of infinity group oids, we can look at pre-sheaves of N group oids, I'll say N minus one group oids. So C will be some infinity category probably small. And I can look at functors on C op with values in N minus one infinity group oids. This is actually the same or equivalent to the full subcategory of N minus one truncated objects in the pre-sheaf category pre-sheaves of pre-sheaves valued in infinity group oids. That's because truncation of pre-sheaves is computed point wise. So I'll write this as pre-sheaves C less than or equal to N minus one. One more fact about this, if you have an infinity category C, then there's a best approximation to an N category. So I'll call that thing the map from C to HNC. So HNC is an N category. And this map is initial among functors to N categories. So it turns out this functor category is equivalent to a functor, always equivalent to a functor category on some N category. So when I talk about pre-sheaves, a category of pre-sheaves of N minus one group oids, I might as well assume that the domain is an N category. Well, last journal, at least I can do that. So we can define analogously to infinity topos the notion of an N topos. So it's the same definition, except that I replaced the role of infinity group oids, pre-sheaves of infinity group oids with pre-sheaves of N minus one group oids. So it's an infinity category E, such there exists a small infinity category of C, an accessible fully faithful embedding of E into pre-sheaves of N minus one group oids, which has a left adjoint, which is left exact. And as I said before, I can actually, without loss of generality, assume that C is itself an N category, if I wish. So, for example, a one topos is exactly, well, the same in the sense that it's the infinity categorical, in an infinity categorical language, it's the same as a groten diktopos. Every one topos in this sense is equivalent to a groten diktopos in the classical sense, because when N equals one, that's pre-sheaves of C less than zero, that's the zero truncated pre-sheaves zero truncated infinity group oids, so really pre-sheaves of sets. A zero topos is exactly the same as a locale, really a frame or a complete hitting algebra. If you start with an infinity topos and you look at the N minus one truncated objects, that is an N topos. That's pretty easy to assume. Remember, let's suppose that our infinity topos, that's easy to prove. I suppose our infinity topos is, let's pick a left exact localization, so presentation is left exact localization of some pre-sheaves category. So I have a full subcategory of N minus one truncated objects in E, but I have a similar thing in pre-sheaves. And remember that truncation is characterized by a condition on the iterated diagonal, so it's a limit condition, a condition in terms of finite limits, and both L and I preserve this condition. And therefore they preserve truncated objects, therefore they restrict to functors on these subcategories, which are necessarily have the appropriate properties as you can prove. Certainly I is fully faithful, you can show it's accessible, and L is still left exact. In case for any infinity topos, the zero truncated objects are a groten-deak topos. And the minus one truncated objects, which is the same thing as sub-objects, so the terminal object is a local, opposite of a local. Furthermore there's a fact, I won't try to prove it now, but any N topos is an N minus one truncation of some infinity topos. I'll warn you here, so when you have an infinity topos E, you will call E less than or equal to zero the underlying one topos. But that is not a complete invariant, you can certainly have different infinity topos, which have the same underlying one topos. Easy example comes from infinity group boards, take your favorite infinity group board, then you can form the slice over that infinity group board and that is an infinity topos. Now I can take the zero truncation, that is equivalent to the functor category from the fundamental groupoid of your space into sets, that's the fundamental groupoid. So the zero truncation of this infinity topos only depends on the fundamental groupoid of X. However, the infinity topos itself actually depends on X itself. The fundamental groupoid is certainly not a complete homotopy invariant of spaces. Therefore for any infinity topos we get this chain of full subcategories of objects with various truncation levels, and we have left adjoints going back, which are called truncation functors. So at this point I'm going to return to this question that I introduced in the first lecture, which is where the second lecture I guess where the growth and deac topologies in this game. So I have to think generally about left exact localizations. Let's first establish some terminology. So by a localization and I think reflection is a better term here, but it's sort of standard to call localization. So it's a picture like this you have a fully faithful embedding with a left adjoint. I can identify because it's fully faithful I can identify D with its essential image and so in practice I will just do that I will assume that D is a subcategory. When you have a localization you have something that I'll call the kernel this may have some standard name but I couldn't figure out what it was I'll just call it the kernel. That's the class of morphisms and E that are inverted by the left adjoint. So it's the class. So it's the class of morphisms that it'll takes to an isomorphism. Any kernel has the property of being strongly saturated assuming he has co limits. Isomorphisms of course are in the kernel logically. It has the two out of three property. So, if I have two morphisms and a composition and any to. And T implies all of them are empty. And lastly this class this kernel is stable under code limits computed in the arrow category. So if I compute a column in the arrow category. It's actually also T. So every localization determines a strongly saturated class, you send the localization. It's a that's an injective correspondence in the sense that from the kernel you can recover the localization. The full subcategory is the class of what are called local objects. So it's the class of objects, such that the map induced by mapping by any T, going to access an isomorphism for every morphism in the class T. If he is a presentable infinity category, then you can classify the accessible localizations using the theory of presentable infinity categories. These correspond exactly those strongly saturated on classes that are generated by a set. So T equals s bar for some set of morphisms size restriction. So this s bar is the strong saturation of s. It's the smallest class of morphisms containing s and closed under those properties. Isomorphisms two out of three columns. So this is a correspondence for any set, you can build localization whose kernel is the strong saturation that set. If I want to think about left exact localizations. So those are going to this should probably be accessible. And these are strongly saturated classes that are the saturation of a set. But the left exact property corresponds to the classes where the kernel is in addition closed under base change it's closed under taking pullbacks along the map. And that's proved by an elementary argument which actually works just as well in the one category setting in general. Right. Okay, so the key question that one would like to answer and have a good answer for if you have an infinity topos, how do you classify the left exact localizations. There's some things to say about this I will not say everything there is to say. I think there's going to be a talk in the conference next week about this exact topic, but I'll tell you a little bit. So, let's suppose I have an infinity topos. Let's suppose I have a left exact localization, and I'll call its kernel T. So that T gives you a local class I think of the kernel as a thing of it as a full subcategory of the arrow category. So I'll take the intersection with the Cartesian arrow category. The intersection is a local class. That's actually very straightforward to prove using the left exactness of the localization certainly closed under base change. And it's closed under a co limits in the Cartesian category because in fact it's closed under co limits in the arrow category. As a consequence we have the following if I have a pullback square where I'm pulling back along a cover. F is in the kernel. And so is G. So that's a property of kernels because they are local classes. Now still assuming I have an infinity topos in the left exact localization with kernel T. I have the following interesting condition on elements in the kernel. If I take a morphism F, and I make its cover mono factorization so I is a monomorphism P is a cover, then the morphism is in the kernel. The morphism F is in the kernel. If and only if I is in the kernel and the diagonal of F is in the is in the current. So this is a more or less elementary argument using left exactness. I'll give some, I'll give it sort of very briefly. So in one direction suppose F is in the kernel. Well, that means that L of F is an isomorphism. L is the sheification, the left actor. L of a monomorphism is automatically a monomorphism, because it's a left exact localization. The hypothesis is that L of F is an isomorphism. And now all of a sudden when I apply L I've got a monomorphism, which has a section, the inverse of L of F composed with the with L of P. Well, it is true even if any categories that monomorphism with sections are isomorphisms. You know, this tells you that I isn't T. L of I is an isomorphism. And the other property is straightforward because L is left exact. The diagonal of L is L sorry L of the diagonal is the diagonal of L. So you can use that to show the delta F is T. Okay. So first of all, if I want to show that if these two things are true, then F is in the kernel. So first of all, if I form, if I think about the diagonal of F, which is a map from a times over VA. I can factor that through the diagonal of P where P is part of this mono cover factorization. The second map in that factorization is actually a pullback of I, in some sense, it is itself a monomorphism. And because it's formed by pullbacks from I, and localizations left exact. And since if I assume that I isn't even so is J. And since I'm going to assume here that the diagonal of F is in T, I actually have the diagonals P is in T. And I get to showing that F is in T. Well, I also have this diagram on the bottom. Here's the diagonal of P. It maps to this pullback, which is the square on the right. Well, if the diagonal of P is in T, since it's factors with Q, it factors the identity two out of three implies that Q is in T. Oh, but now I also have this P here, which is a cover. And I just prove this property that if this class this property of being in T is local. So because P isn't is a cover and Q isn't T I get that P isn't T. And since I've already assumed that I is in T. That's where part of my hypothesis the composite is T. Just I'd go through that argument. I don't think I didn't use, don't think I really used anything here that wouldn't work in say a one purpose. As a consequence. If I have one of these left exact localizations of an infinity topos with Colonel T. And for any in any finite in the, well, I haven't defined that for infinity but the intersection of T with it with the class of in truncated maps is determined entirely by the intersection with the monomorphisms, or to make it more explicit. If I have an in truncated map, which means that it's in plus two iterated diagonals nice and morphism. And the kernel, if and only if the sequence of maps I zero I one up to and I n minus one is in T, where those are constructed inductively, I guess like this. So these are the coming from let's just call this okay. These are parts of the cover mono factorizations of the various iterated diagrams. That's the, that's what we've learned here. Let's make a definition. This definition is due to Larry, a topological localization of an infinity category is a left exact. I should have also said accessible here. Actually, I don't have to say accessible. Every left exact localization of a left exact localization. Sorry, a topological left exact localization. A topological localization of an infinity categories is a left exact localization whose kernel is generated by some set of monomorphisms. That's a definition. And the theorem you can prove is that every left exact localization of oops, I should say something's a little bit wrong here. And that's because of an end of an end topos every left, left exact localization of an end topos with and less than infinity is topological. That's a combination of the fact, the fact that I proved here that the class, the kernel, the intricate maps and the kernel determined by the ones that are monomorphisms and the fact that all maps. In the category like an end topos are truncated at some level. They are all in fact in truncated in minus one truncated doesn't matter. They're all finally truncated for some given value. Okay. What we're actually interested in are the topological localization of the pre-sheaf category, meaning pre-sheaves of values and infinity group loads. So if I have a topological localization by definition that means that the kernel is generated it's the strong saturation of a set of monomorphisms. Now monomorphisms form a local class. In the pre-sheaf category we have a collection of objects which are the representable pre-sheaves and they're generators for that category into the usual sense, the infinity category. Everything's a co-limit of some small diagram of representables. So if I have a topological localization, I can argue so that I can replace my set S with a particular kind of set, a set of monomorphisms whose targets are the representables. I actually have to use the fact that the kernel is a local class in order to do this. So what I learned is that every topological localization of pre-sheaves determines a Groten-Dick topology on the infinity category C. So what's a Groten-Dick topology on C? Well, you can define it as a collection of sieves, that is to say a collection of sub-objects of representable pre-sheaves, which satisfy a list of properties which I won't give, but it's a standard list of properties that is familiar as one of the standard ways of describing a Groten-Dick topology on a one category. Very often people choose to describe the topology using a different language, using covering families, but any family of maps to an object can see determines a sieve. I'll note here that this is an infinity analog of the notion of a Groten-Dick topology, but it doesn't actually require any deep ideas. These are actually in bijective correspondence to Groten-Dick topologies on each one of C. So remember every infinity category has an associated initial one category that it maps to. It's called the homotopy category, the infinity category. And so in fact, Groten-Dick topologies on C correspond to Groten-Dick topologies on the homotopy category. So they actually correspond to conventional Groten-Dick topologies there in the usual sense. That's because you can read off sub-objects of representables from the homotopy category. And the conclusion is that every topological localization of pre-sheaves is of the form sheaves C S for some infinity site. So associated to an infinity site, which is an infinity category with a Groten-Dick topology, you can describe a full subcategory of sheaves. This will be exactly the collection of pre-sheaves. This is an isomorphism for every morphism in the set S of things in the Groten-Dick topology. So that characterizes the topological localizations of pre-sheaves. Now I can do something similar when n is less than or equal to infinity that as I look at localizations, left exact localizations of pre-sheaves of n minus one group whites. In this case, every left exact localization is topological. I think I said something like that here. So here, every left exact localization is a category of sheaves for some insight. So here C is an n category and S is a Groten-Dick topology on the n category. If n is less than infinity, everything is a category sheaves on a site. In the case of n equals one, this is the classical statement about Groten-Dick topology, which is usually actually taken as the definition. Now, of course, I've emphasized that in the infinity case, this is only the case for the topological localizations. So in notion of cotopological localization, what's a cotopological localization? A cotopological localization of a presentable infinity category, that's an accessible left exact localization with the property that its kernel is such that the only monomorphisms in the kernel are the isomorphisms. So it's sort of as far as you can be from being topological. And then you can show that an accessible left exact localization of an infinity topos is cotopological, if and only if its kernel is contained in the class of infinity connected maps. The proof I won't write it out, but it's by the same ideas that I've already shown that show that the topological localizations are determined by monomorphisms. Actually, there's a sketch of a proof here, but I'm not really going to give the full details. In one direction, it's obvious. If the kernel is consistent, actually in one direction, it's obvious. If it's cotopological, then well, you already know the infinity connected maps are, which are monomorphisms are the isomorphisms. In the other direction, if you have a, if the kernel contains any connected maps, you have to show it's containing the n connected maps for all in what I'm going the wrong way around. I think this page is again messed up somehow, proving this direction. You're approved this direction. Very good. So if you have a cotopological localization, you first show that all elements of the kernel are covers. And to do that, you just use the epi-mono factorization or the cover mono factorization of f. If f is in the kernel, well, that means that i is a monomorphism. We've seen this before, but l of i is a monomorphism. Therefore, an l of f is an isomorphism. But you can use that therefore to show that l of all these things are isomorphisms because you have a monomorphism with a section. So, or sorry, you can use that to show, oh, it's cotopological. This shows therefore that i is in t. But therefore, because it's cotopological, i is an isomorphism. Therefore, f is a cover. And then there's a similar argument that works inductively on n to show that t is containing the n connected maps for all n. You have to use a fact I haven't proved. It's the fact that if you have a cover, then f is in connective if and only if it's diagonal is n minus one connected. This is sort of an inductive argument that sort of comes ultimately from the inductive definition of truncatedness. Let me give an example of such a cotopological localization. If we use an infinity topos, we say that an object is hyper complete. If its projection is orthogonal to all the infinity connected maps. This determines a full subcategory of hyper complete objects. And that full subcategory is an example of a cotopological localization. The kernel of this localization is exactly the collection of all infinity connected maps. So this is in some sense, the maximal cotopological localization kill all the infinity connected maps. So it's a formal consequence of these definitions that if you have an in truncated object, it's, which is, it's automatically hyper complete. So the in truncated hyper complete objects are all the hyper, are all the in truncated objects if n is finite. So this hyper completion is is a phenomenon does it does not is not seen from finitely truncated objects.  So for example, this, this example that I gave not in the previous lecture but earlier. Well, previous hour I guess, of a particular topological space with an object that's not infinity connect that's infinity connected. That's not trivial. That's an example of an infinity topos that is not hyper complete. It has a non trivial hyper completion, because it has non trivial infinity connected maps. Now there's a theorem, which does describe all the accessible left exact localizations of an infinity topos they all factor essentially uniquely as a composite of two localizations. A topological localization. And then there's a co topological localization of that. So as a consequence, every infinity topos is a co topological localization of sheaves on some infinity site. So the idea is that he will be a co topological localization. The way it works is that ill inverts, at least some infinity connected maps. So, anyway, the consequence is that not every infinity topos issues on a site, but there is this co topological. Everything is a co topological localization. I should mention here is a historical thing so there's actually a class of infinity topo that were constructed. Before the infinity categorical language by entre all, then by Richard Dean. These are model categories of some official pre sheets on a one site one site. These model categories give you infinity categories and these actually give you hyper completions. They construct the hyper completion of what I'm calling sheaves on the site, sheaves on the one site viewed as an infinity site of course. The one site is actually a kind of infinity site. So, um, that's because if you look at their construction they actually define their weak equivalences in terms of a notion of homotopy group. Their notion of homotopy group cannot see infinity connected objects. So by the nature of homotopy groups. This ultimately leads to a question is every infinity topos equivalent to some infinity category of sheaves on an infinity site. It may seem like I've told you the answer is no. But what I told you, um, is that there are examples of infinity topo way, which I've constructed, you know, which admit non trivial co topological localizations. In some sense the proofs I've given you tell you that the canonical site. The canonical site of an infinity topos might not give it to give give you might not have E as a topological localization. The obvious thing topological localization. The obvious thing to do is to take a large, you know, a small but a full subcategory review that's closed under finance limits show that it's a left exact localization appreciates on that that's a canonical site. Those are often not topological localizations for a random infinity topos. So it's an open question, I believe as to whether this is true. I thought for a long time this, of course, the answer is no, because look at these examples I have but they weren't actually examples of this. It seems very hard to address that question, because I don't know anything that distinguishes the infinity topoi which come from infinity sites that are she's an entity site I don't know of any property those have that something else might not have. So I don't even know where to start to try to prove this. So it's in principle it's possible that the answer is yes I think the answer will likely be no but who knows. Okay. I see here I'm going still going a little bit over on time. I do want to talk about geometric morphisms. And this is very straightforward because you just do the things that work for one topoi. So a geometric morphism is between infinity topoi is a functor. It's an adjoint pair of functors, whereas the left adjoint is in fact left exact there's finite limits. This gives you an infinity category of geometric morphisms the notations people use here are fun lower star from E to F, but you can also have fun upper star from F to E. And that depends whether you prefer to think about the left adjoint or the right adjoint. This also gives you an infinity category of infinity topoi. So this has the property that the space of maps of infinity topoi from E to F is the maximal subgroupoid of this functor category. Of course, these are potentially large. And this is a large infinity category. In general. I actually showed you the recipe for computing geometric morphisms last time. To compute, for instance, a geometric morphism to pre chiefs on something. So let's compute the fun upper star so the left adjoints. So those are going to be the color preserving functors which are also left exact. So that's a full subcategory of the category of color preserving functors on pre chiefs are the coolant completion of C. So color preserving functors from pre chiefs are the same as just functors from C. The inverse is the left con extension. And you can describe what this full subcategory is these are the functors, color preserving functors such that well, they satisfy these conditions that I gave it takes the terminal object to the terminal object, and if preserves the pullbacks of co spans of representables. Rose. So this remarkably nice set of conditions. Consequences, well an immediate consequence, there exists a unique geometric morphism to infinity group oids. So that thing there is the terminal infinity topos infinity group oids. If you have an infinity topos a point is just a geometric morphism from us. So as you can do in one topoi, you can say that infinity topos has enough points. If the left adjoints, the stock functors for all points are jointly conservative. But there's a warrant warning that comes in here and it has to do with the fact that infinity group oids are hyper complete. So the infinity connected maps and infinity group oids are just the isomorphisms. So if I define having enough points in this sense, then he can have enough points, only if it's hyper complete. The stocks cannot see infinity connected objects, because if any group oids doesn't have any. In fact, in practice. At least if you look at some of the things that Jake has taken where he has done you take as a definition it has enough points. If it's hyper completion has enough points in the sense I've described. So that's an additional issue that shows up in the setting. Of course, even for a one topos, you could just fail straight up fail to have enough points. Oh, here's if you want to compute maps into a slice there's a recipe. Maps of infinity to those F into the slice of you over X, which is also in the topos that corresponds to GMM metric morphisms to E together with a section of the pullback of F in F. As a consequence. This actually gives you a fully faithful embedding of your infinity topos into the slice in infinity category of infinity top away over E. So if you just send an object to its slice together with its forgetful function to E. Oh, here's one more example. Torsers, this is sort of the classic example of a geometric morphism. Let's take a small infinity group or it might be easier to think of a group. And let's compute the geometric morphisms from E to pre she's actually compute the left adjoints. Okay, so these are going to be the, the, the funkers from G up to E, which satisfy my conditions takes the terminal object to the terminal object and preserves pullbacks of cost bands of representatives. They're automatically satisfied, because group oids have pullbacks. They just do, because everything's an isomorphism. So I only actually need the first condition so this will correspond to the funkers. P, such the co limit as a functor on G, I guess on G op is the terminal object. And actually the correct definition of a G torsor in the context of infinity topoi. This may not look like what you would call a G torsor. But here's why. This condition is equivalent to the following will certainly implies the following. First of all, if I have such a functor, and I have this property so that it's co limit is the terminal object. I obtain a cover as a morphism of E I take the co product of all the values of my functor at all objects of G. And the map from the co product is a cover by the general property told you before. Second of all, I have another thing that comes from descent. So let's suppose I have one of these P with this property. Let's consider for any pair of objects in my infinity group or a G. I can associate to that a map which you can think of as the action. So I have px, p y, and then I have the infinity group of maps from y to x in G, I guess in G. I can pull that back pie here is the projection is the unique geometric morphism training group or it's. So if you like this is a map P times G to P, if G is a group pullback G. It's the action map. This fits together. If I let why vary. So this actually is a functor gives me a functor from G up to my infinity topos the value at y is whatever and above. The X is fixed. So this is for each x p of x times p star the pullback of the representable pre chief on G to E maps to P. Now I can form the co limit with respect to G up. By definition because it's a G torsor the Coleman of P is the terminal object. You can compute the Coleman on the left hand side using university universality of co limits to get rid of this factor that's just constant. That's really p of x times the Coleman of the representable. So lots of representable funkers are terminal and pie star preserves co limits. So in fact this is just p of x. That's the co limit of that current transformation. Now the thing about this transformation it's actually a Cartesian natural transformation of funkers from G up to every morphism and G. You get up the you plug that into the transformation you get a pullback square and that should be just because it's an infinity. It's a group boy. You get a square where both arrows are isomorphisms. Well now I have descent. Descent tells me if I form this co limit and then I pull back again to each object. I get a pullback square. So I have a pullback square for every X and Y. If I write this out just for a group. So this P times the pullback of G to P to P to one is a pullback. In other words, this thing is equivalent to the product of P with P by sort of a tautological pair of maps, which are projection. And if you like the action that recovers the classical definition of a torsor in the one category case but it's a it's in some sense a different definition in the infinity category case. The torsors that oddly have a much easier deaf cleaner definition infinity. Alright, I'm very low on time. Let me run through a couple of one remaining topic. There's something called n localic reflection. So I have an infinity category of infinity to boy. And there's a functor, which is given by take your infinity topos and restrict to the full subcategory of n minus one truncated objects. That admits an adjoint which hopefully this is correct is a right adjoint. I'll call this R and F, let's call the n localic reflection, you can always promote for any in an end topos to infinity topos in a canonical way. And here's the formula if I start with an end topos. We said that those were always categories of sheets. So we have a category of n minus one group boards on n minus one site. I can actually pick this so that the underlying category see has finite limits. So the recipe to compute the n localic reflection is you pick such a site with finite limits that presents your end topos, and then the end localic reflection is sheaves of infinity group boards on the same site, which is also an infinity site. I'm consistent. So that's the formula for n localic reflection. Everybody forgets the fat well I always forget the fact that it has to be you have to use a category of finite limits otherwise you get the wrong answer. Okay. So I'm at the end of my time. I'll notice one more property here. So you can define co homology of infinity topos. So I have this unique morphism geometric morphism to infinity group words. So I have a pair of adjoint functors constant and the constant pre chief and the global sections. So if I take an island where McLean space in spaces. I can pull that back to eat and then push it forward again taking global sections, and then that defines the co homology of my infinity topos with constant coefficients which are in a dealing group will take the appropriate homotopy group of this thing I can use various in here, which are bigger than J. Notice I remember McLean spaces are in truncated. So this invariant it's certainly not a complete invariant, but it certainly does not distinguish on say E from its own hyper completion, because the pullback of the only more plane object is already going to be in truncated. The same answer for both in a type of completion. So this idea does lead to a very nice formulation of the idea of a shape of an infinity topos. Using this projection q, you get this composite functor. q, upper star falling q lower star. And this isn't an example of a functor from s to s. And it's in a full subcategory which is called pro s, which we can define to be the collection of functors from s to itself which are left exact, or more precisely defined to be the opposite and also it turns out a category of inverse limits of representatives of filtered interest limits so it's reasonable to call it pro s. It has a topological embedding by s itself by the native functor. Every infinity topos has a shape, which is a pro space in the sense, and you can prove for instance that if x is a nice enough space if it's para compact. Then shape of she's on x. Notice here I'm using space in the sense of actual topological space. If it's para compact and its shape is in fact determined by its underlying homotopy type. The next here is the infinity group void, which is the homotopy the usual homotopy type of the topological space x. Every topological space has a homotopy type that you think of as an infinity group. So para compact topological spaces have sort of classical shapes, but there's a general theory of shapes. Since I'm out of time I'll have to stop I wrote down some pages that talked about applications. One is you can talk about she's of infinity categories on infinity topos.  I can take five minutes and just fill in these pages. Yes, maybe just five minutes I think it's quick I can just fill in the definitions. I have an infinite category that's complete we can just define a she's on E with values and a to be a functor from E op to a, which preserves all limits, all small limits. If he is she's on a site, you can reinterpret this as in sort of a more conventional way she's on a site. And for instance, I can define things like she's of infinity categories, maybe large ones, even on E. So the example I wanted to mention is like the type of example that I mentioned in the very beginning, just to be specific if I have a scheme. I have for every open set some derived category of quasi coherent she's that's the one category. This doesn't form a sheaf. But derived categories come from infinity categories that derived category is the homotopy category of an infinity category. And the relation that sends you to its derived infinity category is in fact a sheaf in the sense this provides a language for talking about she's infinity categories. In some sense this is interesting even if he is just a one topos. Of course, if you have a one topos you can promote it to an infinity topos, and then talk about sheaves of infinity categories and infinity topos, and this is already useful in classical settings. You know, talk about these kinds of derived categories and people are doing that. The topos were really introduced by these authors for talking about derived geometry. So if you have a some category of ring like objects, which could be commutative DGA's or infinity rings vector if you like homotopy theory, then you obtain a notion of a ringed infinity topos and infinity topos together with a sheaf with values and a one of these categories of rings, and this leads to a notion of derived geometry. And to be honest, most of the interest is in this this category of generalized rings, but it's in some sense you need this notion of infinity topos in order to make sort of decent definitions. Differential comology this turns out to be a sort of an area where these have turned out to be useful. So in general comology, these are invariance of smooth manifolds that combine things like singular comology, say with the inter coefficients with Durham comology with the comology represented by differential forms. So what you can do is you can form an infinity topos. You can form a gross infinity topos a growth infinity topos of sheaves of infinity group oids on the large site of see infinity manifolds, which is actually essentially small so it's fine. This contains objects like a little bit of a plane objects which represents actually the singular comology of manifolds, but it also represents contains objects like omega n, which represents things like differential forms. And you can combine these to give things that represent differential comology. So this is a nice context where they're useful. Here's a page where I couldn't think of anything useful to say on one page so I won't. There's an interesting recent work by barric glassman and hey, and a paper called ex exodromy. I don't know how to pronounce the word exodromy. Which uses stratified infinity topoi and theories of constructible she was an infinity topoi to do some kind of generalizations of a sort of classical gal off theory in the in the context of algebraic geometry. Finally, I should mention the logical aspects of infinity topo and I didn't want to take much time in this because I don't understand this very much. So in one topoi. One topoi have an internal language. There's something for instance called the Mitchell Benabu language and that has an interpretation in a one topos. There's a notion of type theory due to Martin look called dependent type theory, which has an interesting aspect it introduces types for identity, instead of just having a sort of a relation. We have an identity type between any two terms of some other type. It also in many formulations introduces type families. So there's some sort of universal type. And it was noticed that these identity types behave like spaces of paths in a space, which suggests a homotopy theoretic interpretation, which was developed by everybody and Warren and boy volume of Ravadsky. And which led to the notion of univalent type theory. Let me not try to describe what univalent type theory is because honestly that's a whole lecturing itself and when I'm not competent to give. But we've asked he showed that infinity group points that is some official sets for my model for his univalent type theory. The univalent type theory has this universal type and that core corresponds to what I called the object classifier that the base of the universal morphism classifier. More generally, in fact it was early recognized that this was true and it's been proved by shulman that in some sense every infinity topos is a model for univalent type theory. So you can say that univalent type theory is the internal language of an entity topos in some sense. But you do have to be careful with that statement there is an issue here. It's not really an internal language in the way that I've been talking about infinity topoi. Type theory, including this univalent type theory that has functions, which can be composed, and that composition is actually associative on the nose. It's built into the way functions are described because they look like kind of look vaguely like functions of sets. So any model of such a type theory must be a one category. Must be a one category. That's the sort of model that these people have constructed. They've constructed models that are, for instance, a Quillen model category, which is only a one category. But the Quillen model category structure is used in describing how the model works. Fibrations play an important role. And so this theorem really says that it's a Quillen model category that can be chosen to be Quillen model categories whose corresponding infinity category, the infinity category you can extract from that one category is an infinity topos. So that's the sense in which every infinity topos is a model for a univalent type for univalent type theory. It's via one of these Quillen model categories and the interpretation is actually in the one category. I don't think anybody knows how to make this kind of linguistic or language or internal language that describes doing infinity category theory. This isn't really something I think anybody's really figured out to do in sort of a way that seems practical to me. So I think that's something that's an interesting subject if you like those things. All right, that's all I had to say thank you. Thank you so much for this very nice and very rich course.


All right, you guys are in for a treat because you get Mike Piper back up here If we can tear him away from the drinks there in the back. He's back there serving drinks But let's get him back up here. He's gonna talk about Investing in a simple manner and the best thing about this with Mike is that he practice what he preaches and Thing I love about Mike is I am still learning stuff from Mike I sent him an email just last week to clarify something. I did not understand He sent me back an email filled with algebra He totally understood it and so it's great to have Mike as a resource. Luckily. He's not gonna be talking about algebra I hope in this presentation, but it should still be well worth your time and attention All right invest with simplicity Back in 2008 or Alan can correct me if I'm wrong in 2009 perhaps In his book how a second grader beats Wall Street He outlined what he called the second-grade or portfolio and this was a portfolio that consists of a total stock market index fund a total international stock index fund and a total bond market index fund and you keep hearing about this portfolio now We just call it the three-fund portfolio and it's become largely a default investment recommendation among the Bogleheads community And the reason it's become so popular is because it's really simple and it's extremely well diversified just like you know Alan and Christine were showing you it includes Thousands of stocks from around the world and a diversified collection of bonds with just three mutual funds And in some cases for some people it can make sense to go one step simpler You can use a one-fund portfolio that would include something like a target date fund a vanguard life strategy fund That's what I use or a balanced fund a lot of fund companies offer those. They're very straightforward They typically just have a fixed 60% stock 40% bond allocation But if you're considering using a one-fund portfolio, it's important to keep a lot of different things in mind before making that decision Number one is that it's still important that the fund has a low expense ratio That matters with these funds just as much of it as with any other mutual fund high expenses are going to eat into your returns number two It's really important to take some time to check the actual asset allocation for the fund as well as the Glide path, which is how the allocation is supposed to change over time Look into that rather than just relying on the name of the fund For example, if your 401k has a 2040 target date fund and you're planning to retire in 2040 That fund might not be a good fit for you Your personal risk tolerance could be much higher or much lower than whatever this fund company assumes is Typical for somebody retiring in that year because there's more to risk tolerance than just what year you plan to retire so it's important to just look it up on the fund company website or Morningstar or wherever and See what the actual asset allocation is and see if that's a good fit for you because maybe again using the 2040 example Maybe the 2030 fund or the 2050 fund is going to be a better fit for your personal risk tolerance and Finally, the last important thing to keep in mind about all-in-one funds is that they aren't a good fit for taxable accounts We were just talking about using tax efficient funds in a taxable account All-in-one funds are not tax efficient. There's a few reasons for that Reason number one is that they use taxable bonds whereas for some people tax exempt municipal bonds would be a better fit Reason number two is they get in the way of asset location Remember asset location the whole idea is to make sure to only own tax efficient things in your taxable accounts Well with an all-in-one fund the whole point is to own everything So it's going to include some tax inefficient stuff in that taxable brokerage account, which isn't ideal and number three is That the third reason they're tax inefficient is that this Fund of funds structure so a target date fund that owns underlying mutual funds It adds another layer of turnover right if you imagine for example the Vanguard target date funds They've got four underlying mutual funds a US stock fund international stock fund US bond fund international bond fund And each of those four underlying funds has its own level of turnover and so that creates some taxes But then the target date fund that owns those funds Has its own turnover Because it has to rebalance among those four underlying mutual funds and that creates some additional tax costs for you as well And sometimes you'll see a case not going to name names, but a particular fund company This year switched one of the underlying funds in a significant way It created a huge capital gain distribution for shareholders. It was really expensive So these again target date funds life strategy funds, they're neat They're great in a lot of cases, but they're not a good fit for a taxable brokerage account But why do we talk about investing of simplicity at all like why did this make it onto the list of Boglehead's principles? Because rebalancing isn't frankly all that hard if you can use a spreadsheet you can do it You can even do it with pencil and paper and a calculator if you know if you're inclined to do that sort of thing but simpler portfolios do save you time They take less time to rebalance and if you're using an all-in-one fund like a target date fund They completely eliminate the job So the example I always use is I compare it to doing the laundry, right? It's not like that's a really challenging job But it would be nice to never have to do it That's what a target date fund does it just removes this chore from your life and that's nice But really that's not the most compelling reason in my opinion That's not the most compelling reason to use a simpler portfolio The simpler the the better reason for a simpler portfolio is that it improves investor behavior And to talk about that I want to highlight this study that has come up Allen mentioned it also It's morning stars mind the gap study and they do this study every couple of years and every time they look at the last 10 years of mutual fund performance and They look at all of the different mutual funds that morning star looks at so however many thousands of funds that is And for each mutual fund they look at two things First they look at the regular reported performance figure for that fund, right? So that's just the 10-year return figure that you would see on a fund company website or in a prospectus or in a brochure Something like that and then the second figure that they calculate is what they call the investor return And this is a dollar-weighted figure so it accounts for The cash flow that's coming into the fund or going out of the fund when shareholders buy and sell shares And so the idea with this investor return figure is to reflect the actual return That the average investor actually earned in this fund over the period in question So if we consider a hypothetical actively managed fund Imagine it's brand new at the beginning of those 10 years, right? And so because it's brand new and that's also say it's from a brand new fund company So nobody's heard of it and has almost no assets under management and imagine that for the first four years of the 10-year period It has excellent performance just incredible returns And so during those four years people start to hear about it, right? It gets written up in some articles and so on and so a bunch of money comes flooding into this mutual fund and Then in our example here, let's imagine that over the last six years of the period It has really mediocre performance Well the regular 10-year performance figure the 10-year return figure for this fund Each of those 10 years is going to count the same as the other 10 years So it's gonna have a pretty good 10-year return figure because those first four years were so good But the investor return figure is not going to be as good because those first four years Nobody owned the fund during those first four years So they won't count for very much in the calculation and the last six years with the mediocre returns That's when most people learned owned the fund. So that's what'll count for most of the calculations So in this example, you'll see a good 10-year return and a really mediocre 10-year investor return there's gonna be a big gap between the two and that's why they call it the mind the gap study Because we're looking at that difference and the point is that that gap is a measure of how well investors do With the timing of their buying and selling of the fund So in our example here this hypothetical fund This big gap is the result of the fact that investors did a terrible job with the timing of their purchases, right? They bought after the first four good years and right before the six mediocre years. So there's a big gap Now where I'm going with all of this if we look at the most recent edition of the study So it came out this year and it looked at the 10 years ending December 31st of last year These are the gaps for the different categories of funds and the two things I want to highlight here Or that the gap was smallest for allocation funds. That's basically things. So that's morning starts term It's basically things that include stocks and bonds within the same same mutual funds So balance funds target date funds life strategy funds and the gap was largest for sector equity funds That would be things like a technology stock fund or a healthcare stock fund and Because they do this study every couple of years, of course the exact figures the exact percentages Change right from one edition of the study to the other but this overall relationship is very consistent Every time we see that investors do well with allocation funds And to me that's not the slightest bit surprising because if you think about a target date fund imagine you're using that in your 401k All it is is one fund. You just put money into the same fund There's no temptation to move your money around right the whole point is to put it on autopilot And so a lot of people do that they put it on autopilot and that actually works really well and Then the other thing we see every time is that investors do really poorly With sector equity funds and again to me that's not surprising because when you see portfolios it includes sector equity funds They're usually portfolios that have like 30 mutual funds or something insane And so when that's what your portfolio looks like there's a huge temptation to Move your money a little bit this way or a little bit that way or get rid of this fund now that fund and that's not to say that you know you personally would do that but There is you know very clear this data from Morningstar makes it very clear that investors do that and it's generally To their detriment and they do it more often with funds that represent narrow slices of the market Then they do with more broadly diversified funds and that's true all the way up to the most broadly diversified allocation funds Where investors do the best so the study also drills down into narrower categories of funds and Here we're looking at the gap for large cap stock funds meaning funds that invest in stocks of large companies and The gap for large blend funds large blend meaning that the fund is not Specifically a growth fund nor specifically a value fund so it invests in growth stocks and value stocks The gap for large blend funds was about or exactly three quarters of a percent per year The gap for large growth funds was about 1.3 percent per year and The gap for large value funds was about 1.3 percent also It's one of those cases where your intuition could trick you because you might expect that Large blend is basically a blend of large growth and large value, right? So You might imagine that the gap for large blend would be between the gap for large growth and the gap for large value And it's not it's smaller than either of those other two gaps You've got investors doing better with the more broadly diversified funds than with the less diversified funds So why invest with simplicity it does save you time and that is frankly that's nice I appreciate it, but that's not the biggest benefit the biggest benefit is just that it makes it easier to stick with your plan This is a quote from the conclusion of the most recent version of the study the authors wrote This is their italics, by the way, they recommended that the reader focus on holding a small number of widely diversified funds They went on to say that as the fund industry has grown Asset management firms have rolled out more and more highly specialized funds But investors have fared far better by keeping things simple and sticking with plain vanilla broadly diversified funds And then they went on to write that funds that offer built-in asset class diversification So that's funds that include stocks and bonds in the same fund So target date funds life strategy funds balance funds They also excelled in the study not only are these funds easy to use, but they're also easy to live with Investors tend to buy and hold them for long periods or make investments on a regular schedule like in a 401k And that enforces investment discipline and helps them avoid the temptations and pitfalls of trading at the wrong time So that's it for invest with simplicity. I've got Jim coming up in a minute


The Forest of Three. That's what it's called. Nobody knows who named it or when. In fact, this secluded area is not labeled on maps. It has no official name. Only the name given to it by the townsfolk who live on its edge. The Forest of Three. Perhaps it's named after the three tall redwoods that grow on its heart. Three towering giants lifting their heads far above the treeline. They stand in a circle with overgrown branches extended into each other's foliage, as if linking arms. When the wind howls, one can see them sway. Their powerful roots supplying the great forces needed to prevent them from falling. Viewed from the correct angle, it can appear as if they are attempting to dance. To uproot themselves and skip in a circle with hands joined. The three redwoods have been left untouched for decades. Although the ancient well-seasoned wood would surely be profitable for the town's lumber industry, not a single person has ever suggested cutting them down. The redwoods are viewed by the townsfolk as guardians of the forest. As protectors of the town. And a very small town it is. How many inhabitants are there? Nobody knows the exact count. For such details are of little concern. But it could not be more than a few hundred.  Running, skipping, shouting, and all other manners of things that children are prone to do. However, the town itself is a rather boring place, and not the preferred playground of children. After all, the town sits next to a large forest. What better playground could a child ask for? Thousands of trees to climb, rocks to overturn, creatures and insects to be examined. A child could spend every day exploring the vast expanse of green and never happen upon the same tree twice. Yes, the forest is a perfect place for children. A place for them to explore, to imagine, to learn. The children love the forest greatly. They even sing a nursery rhyme about it. Skipping in circles with hands joined, children will chant, Come play, come play in the forest of three. You and I and I with thee. Oh, such fun we have in store. Lurking there. Forever more. Where this rhyme comes from nobody knows. It's possible that the children themselves wrote it. Yet upon examination the theory seems implausible. Forever more. The. Hardly words that a child would understand, let alone include in a song. No, this rhyme speaks of something old, something archaic, something beyond the understanding of children. For many years life was peaceful in the small town. Nothing no worthy occurred. There was no newspaper because there was never any news. A simple lumber town with a simple lumber industry populated by simple people. Everything was as it should be. Nothing was out of place. Then a child disappeared. How long ago was this? Few remember the exact year. Several decades ago at least. A child whose only concern in life was Swedes and playtime simply vanished. A town meeting was called. One of the other children claimed they had seen the missing child earlier that day, that the missing child had gone into the forest to play as usual and had not come back. A search party was immediately organized and sent into the forest. They searched for hours until the falling darkness did not permit them to search any longer. We'll search again at first light. Everything will be fine. It's probably just a game. Don't worry so much. The townsfolk comforted the child's terrified parents. As soon as the first rays of sunlight crept through the trees, the search party was out again. They covered miles and miles, hardly stopping for food or rest. Yet there was no trace of the missing child. Each day they searched and each day they came back with sore feet, hungry bellies, and no child. Hope was still there but it was quickly fading. Each day the search party came back sooner and sooner. Each day they spent less and less time looking for the missing child before heading back. Eventually the searches ceased entirely. If one were to examine the town at the time, at first glance it would appear just as it had before. Men chopped wood, stores had good business, school was in session. Children still played in the streets and in the forest. Of course the family and friends of the missing child grieved, but nothing would seem out of the ordinary. At first glance, look closer and you would see it. The children, they played, they danced. They sang their nursery rhyme. Yet there was something odd about their games. As they skipped in circles, arms together chanting their favorite tune, there was a distinct gap. Where two children should have been holding hands, they instead held their arms to the side, creating a gap in the circle.  During the rainy season, the children often had to play inside. The school had an ample supply of checkerboards, which were excellent at keeping the children's minds engaged. If one looked closely at the children playing checkers, you would notice a single lonely child. Whereas all other children had partners to play checkers with. This child was on their own. Nevertheless, they seemed to be having a fine time, making moves for both sides of the board and even becoming angry when they lost to their imaginary partner. Life in the town continued. The memory of the missing child faded with each year until the other children scarcely remembered them. Soon the children matured and had children of their own.  The adults who remembered the original disappearance were disturbed. The disappearance of another child brought back painful memories. Many of them had been children themselves when the first child went missing, although they remembered very little about that child. Again, a town meeting was called. During the meeting it surfaced that the child was last seen heading into the forest, eager to play. And again, a search party was formed. This search party fared no better than the one 15 years earlier, although the forest was searched each day for hours, with many miles of land being covered, not a single trace of the child was ever found. Again, the search party was disbanded, leaving the family to grieve their loss. After a while, the town seemed to return to normal. Daily life resumed its normal course, just as it had so many years before. Yet if one looked closely at the children, you would notice the same curiosities witnessed 15 years before. The children skipped in circles, singing the nursery rhyme that their parents had passed on to them. But again, there was a gap in their group, a void that was only apparent when they danced. This gap appeared to be just a little bit larger than the one before. Perhaps there was now room for two extra children to join in their happy group. During rainy days when the children were stuck indoors playing with worn out checker sets, there were no longer any lonely children. Each child had a partner to play with. However, laying unnoticed in the corner of the room, there was a solitary checkerboard. It had no players, no children to have fun with it. The pieces were scattered across the board as if a game were currently in progress, yet there was nobody using it. Who can say what this meant? Maybe nothing. Children are prone to strange behavior as any parent knows. A gap in their dancing circle, an unused checkerboard, why should any of these anomalies be cause for concern? In the end, it didn't matter. No adult noticed the slightly unusual behavior of the children after either disappearance. Such was life in the small lumber town. Years continued to pass. Those who were children during the first disappearance became middle-aged. The friends of the second child who disappeared now had children of their own, and life passed by. Completely normal. Until tonight. For tonight is a very special night. If one would have visited the town center, you would find it bustling with activity, worried faces, loud arguments, and a weeping family is what you would find. You see, earlier today a child went into the forest to play and did not return. A town meeting has been called to discuss the best course of action. Many members of the town remember the initial disappearance, which occurred more than three decades ago. Some are saying that the disappearances are connected, that two disappearances could be coincidence, but not three. Some now believe that the forest is haunted while others call them crazy. Early tomorrow morning when the sun begins to rise, a search party will set out to find the missing child. Perhaps they will find the child, and perhaps not. Perhaps the child simply became lost while playing in the forest and could not find their way back home. Or perhaps tomorrow, when the other children go outside to play and begin dancing in a circle, chanting their nursery rhyme. We will see a gap.  And so tonight I invite you to visit the forest of three. Early tomorrow the determined search party will undoubtedly break the calm silence, the quiet serenity of the forest. But for the next few hours, all is still. Stroll through the tall, broad red woods, the thick brush, the moist soil, the trickling crease. Gaze through the foliage into the night sky to see the bright starlight and thin gray wisps of cloud flowing overhead. Eventually you will arrive at the heart of the forest. Here stands three great redwoods, a hundred feet taller and a hundred years older than all others in the forest. They stand with their branches interwoven as if dancing in a circle. The wind howls. The trees begin to sway. Sharp shadows are cast upon the trunks of the great redwoods. The shadows move across the bark and it appears as if the trees are snarling at you, sneering at some great joke that you cannot understand. The wind dies.  Listen for it. The soft rustle of the leaves overhead. The quiet trickle of water through streams. The small animals moving through the brush. Now it comes. So very distant yet so very clear. An innocent chorus carrying a sinister tone. The voice of the forest of three. Come play. Come play in the forest of three. You with I and I with thee. Oh, such fun we have in store. Lurking there. Forever more.


that's another thing most folks don't know like they'll come to me when the trend is over and I'm like bro you got a window man you you got a window let's talk about that window man why is that because you said been talking a lot about momentum yeah this thing like truly why is it so important to catch it in that window you have to because again trend another reason is called a trend because it ends you know what I mean it's a it's a trend for the moment and so most most trends are going to run about 45 to 60 days you know I mean that's that's the lifespan of a trend um and in that moment you have the opportunity to turn that into a hit record you know I mean um thing about is like I like I tell people there are trends there are probably but I don't know 50 000 trends going on right now on tiktok right but out of that how do you take that 50 000 turn the one you're working on into the number one you know I mean and so I think people think it's easy and it's not it's not like when hours and hours just because it's a trend doesn't make it a number one record um justin scott collage just because it's a trend doesn't make it a number one record that takes expertise that takes real know how it takes real money um and it takes real networking and so that's what we've been able to do is we've been able to take those out of those 50 000 trends we've been able to take our trend and make it number one multiple times you know I mean and so if you come to me and this has happened DJ chose he came to me when the trend was over and he actually he came to me when it was going but he didn't want to pay my fee so we put that out there he didn't want to pay my fee I was like bro this is what I charge you know I mean he didn't want to pay so then when it was dying he came like bro I need jobs like what you needed me back then but I was like I think I can help now and fortunate for him and me because I was unsure too I was like man maybe we can turn this around and we were able to turn it around and we end up taking it gold you know I mean um but and he would have came when it was moving it could be platinum who knows see that you know I mean that's what's so important to me because so what I realized working with artists from roundups is when they experience this big crowd yeah they it feels amazing everything's moving right right they're barely touching anything some of them actually like get weird and like step back from everything and just don't do anything like I've heard people say stuff like man you know I kept getting all these comments on tiktok and I just stopped going on tiktok for a while like oh that's yeah but the frustrating thing as someone who's now seen quite a few things is let's just say I've never done 100k streams before all of a sudden this thing in my mind goes crazy and I'm in like two million streams on the song right but you jacquory are like bro this should be 50 million streams right but they don't know that in that window is the difference between it being 50 million and maybe 10 million or 20 million like it's like being in the zone in sports right you really gotta lock in dollars today you're gonna get back 20 dollars in this window usually you put in five and you only get two back today you get 20 but it's not gonna happen for but for so long so like that fee yeah if you're gonna pay that fee but now is the time to pay it right yeah like you got you gotta catch it you gotta catch in the moment it's it's best to catch it as soon as it starts like it's best to catch it from the very beginning because that makes it easier to find the source number one you know I mean um because finding the source is very important is is is very important to find like what started this you know I mean um but catching it from the beginning is best you know but definitely just know like after 60 days it's just about a wrap you know I mean like it's very rare that trend trends happen twice right it's very rare I've seen it but it's extremely rare what when the constant like looking for that source do you have like any special things or usually you just got your team scouting the internet well luckily like um TikToks uh in real search search is is really good you know I mean so it is comes down to the technology you know I mean luckily like the technology is good and it makes it easier to find yeah you know I mean like you can search like key words for like so like there's a song uh I think it's called throw it that's going viral right but the song is you don't need no beat you better hype is hype your best so I can type in hype your best the other and find it versus having to know the name of the song you know what I'm saying it's like so luckily because their their search engine is so good it makes it a little bit easier let me take a quick second to say if you're an artist trying to blow your music up or if you're a manager a music professional in general trying to help an artist blow their music up I have something that's a game changer for you and it's completely free as you may know we've helped multiple artists go from zero to hundreds of thousands of streams we've helped multiple artists go from hundreds of thousands to millions of streams chart on billboard go viral all of that stuff and we've now made the way we've branded multiple artists and helped them go viral completely free step by step in brand man network all you have to do is check out brand man network dot com you apply it's completely free but the thing is we're not going to let everybody in forever so the faster you apply the better your chance of getting accepted brand man network dot com check it out back to the video okay before we leave this subject because you know talking about justine's god at being a tiktok song and obviously way number one people have been talking a lot lately given all this tiktok slander out saying that tiktok isn't it you know it had its moment is done it's so much harder to break songs right right in short my perspective is right yes it was that for a period of time where a few things were just happening the algorithm was open and now it's a little bit harder but it's about doing your job too right yeah what's your perspective on tiktok in terms of like yeah just the the state of tiktok for breaking right music today so yes you missed the moment you know i mean i was screaming at i was telling everybody do not miss this more because i knew it was not going to last this is what people had to understand tiktok is a business just like any other business their their initial goal was to track as many people as possible how do i do that by giving away eyeballs i give away the views meaning that my algorithm is wide open i want to show you to as many people as possible now once you all are here okay now it's time to make the money so now these eyeballs cost now you have to spend money tiktok ads you know what i mean so now you're paying for these eyeballs but with that being said it is a competition who has opened up their algorithm to steal you back from tiktok youtube shorts instagram reels algorithms wide open right now so it's like if you're paying attention you just have to well you have to pay attention like so for example i started a tiktok uh i'm sorry i started a instagram page family page december 24th we are now saturday february 15 16th so about 50 days in i haven't spent any money the page had no problem i started the page at zero in the last 50 days the page has reached 2 million accounts all i'm doing is posting content you know i mean and it's still don't got no followers just like how tiktok you don't have to have no followers all you have to do is post good content and the algorithm is going to make sure it gets seen because they're trying to make you come back from tiktok hey man come on back over here we're giving it away that's what's happening right now so you just got to pay attention to where they're giving away the audience and right now that's youtube shorts and that's and that's reels back to music on tiktok you missed it you should you should have been here when it was popping that we were screaming get on tiktok but you know us black folks we was like oh are they dancing now it's still possible it's just not as possible you know what i mean so it's still there like so on the same token i i started a family tiktok page too um and we had two video i have a video on there that has four million views and i have a video on there that has like a quarter million views so i was still able to get some some you know traction on that page on almost four and a half million views in total on that page um no money spent and see the the thing about that though is like had i been an artist all i would have did was put my music inside of that content and that would and if that if i had done that that would mean in the past 50 days having spent no money 6.5 million people have heard my music you know i mean and i tell artists it's it's it's that simple it's consistency in content content consistently that's all it is you know i mean but also you have to you have to be an artist in a sense of you have to put the music in there indirectly if i'm just trying to flush the music down a throat it's going to be a lot harder but if i'm making good content and indirectly showing them my music in that content then i have a way better chance of them hearing my music and discovering like content is all about discovery i'm using the content to be discovered so for me right now i'm building a family bread so i'm not selling them anything directly i'm just showing them my family i'm introducing them to my family and in the past 50 days like i said about six and a half million people have seen my family you know what i'm saying so it's so possible but don't rely on just tiktok if i had relied on just tiktok i would have missed the two million people over here on reels right you know what i mean so you gotta watch yeah yeah don't don't rely on just tiktok you mentioned justine a couple times yeah and the tiktok and all that stuff you meant and he said something earlier that i wasn't aware of you said the song first came out in 2014 yeah the song was released in 2014 released yeah why do you think it started pop now do you think it has something to do with the grown-ish well well it wasn't that um man that's another lesson i teach artists bro is like you just gotta put the energy out there and and as the more energy you put out there the more possibilities you create for the energy to come back and so justine is a great example that k cam is a good example that so i'll start with justine song came out 2014 right the reason that it has popped again the the spark was uh a content creator that works on a netflix show decided to use the song as part of their tiktok you know what i mean so like they were creating tiktoks for their shows tiktok page they used the song and that was the initial re-entry into people's minds and then from there people took it and started creating with it and that's and so justine had zero to do with it but it would have never happened had she not been putting out music you know and so the same thing i go back to k camp if you weren't like a solid solid k camp fan i think from around 2016 2019 you would have thought he wasn't even releasing music but the whole time he kept putting out and this is probably him at already part of ways and part of ways in 2015 but he was kept putting out music music music music and then some little girl decided to do a dance to his latest song k cam had nothing to do with it but he had everything to do with it because he was constantly putting it out there you know i mean that's what artists had to understand like magic does happen like miracles do happen like you put it out there you never know what individual is going to take your song create one piece of content to it that's going to change your life and so that one uh person that that show hired to make tiktoks change the scene life and that one little girl that decided to make a dance to k camp song changed k camp life again you know i mean and so it's like it ain't always on you you know i mean it's like what what is religious but it's like god will fight your battles and all you have to do is just be present and then you know something to come along without a bless you and just change your life yeah i i like that because the idea of just continue to put the energy out there yeah it sounds like abstract but it really does apply when you put those situations in there and what something to happen with us is so at this point we've had charlie demilio post yeah maybe four or five times never paid her right that's crazy yeah and the first time was completely accident but the next few times there was we had some strategies and kind of like how to increase the possibility but the first time what happened was we had this song on tiktok this is like 2019 um and we're working it it starts to take off and it gets to around 10 000 videos artist budget runs out right the next song charlie demilio finds it before we even really do anything but yeah discover they're do the first song yeah so she never first posted to that first one now you have that person in your vicinity yeah right and console me like justine right she wasn't pushing that song anymore but years later someone went down to rabbit hole of justine because they might have found they probably found a new song they were like what else does she have right and so you never know and it really again it sounds like this abstract thing but it really is practical as long as you know you keep putting energy out there and you know for hopefully you have ownership of that stuff yeah yeah that's another that's another piece to it like you know when she put that song out she was on atlantic but when she left atlantic her mother's an entertainment lawyer so when she left atlantic her mother was able to get those masters back yeah so so she owns that song and so every stream justine spocky that's beautiful