So, today will be the last meeting for categories and punctives, today we shall demonstrate how certain classical constructions in mathematics can be put in categorical language beneficially. Like any category, an object in this category is called an initial object. If it admits exactly one morphism into every other object, say A is an object, then MAB must be a singleton set for every B inside C. So, it is called initial object. Exactly due to this, if A admits exactly one morphism from every member B into itself, then we will call A a terminal object. So, it is same thing as saying M B A is a singleton for every B inside C. If A happens to be both initial object and a terminal object, it is possible of course, then this is called a zero object. So, this terminology is again copied from like abelian groups or any other abelian kind of things or even groups theory also like rings, fields and so on. So, we will see why these these terminologies help us and how they help us. In the category of all sets, the empty set is an initial object, but it is not a terminal object. Also, every singleton set in ANS is a terminal object, but not an initial object. Categories such as the groups, abelian groups, vector space over a field, R modules, etc. They all have zero objects. The zero space or whatever the zero group will have exactly one homomorphism from it to any other group. Similarly, there will be exactly one homomorphism from any group into the trivial group, zero group. So, zero element which is if we multiply it, if you write it will be the identity element, the singleton identity group is both an initial object and a terminal object. So, this is called a zero object. There is a simple way to turn initial object into a terminal object by considering the opposite category. In category C, if A is a initial object, category C of it will become a terminal object and vice versa. So, you see, ENS, ENS had an empty set as an initial object, but not a terminal object. But if you take ENS of it will become a terminal object, but not a initial object. So, it is easy to produce categories which are, which may or may not have any initial object or may have many of them also and so on. In any category, it is easy to see that any two initial objects are equivalent in the sense of that category. So, this is simple observation which helps to understand many part of mathematics very easily. Likewise, a terminal object will be also unique if it exists. Unique is a sense of equivalent class. Equivalent, within that category, they will be equivalent or you can say isomorphic or whatever. Now, a zero object has some more structure inside it. For every A, B inside C, there is a special morphism 0, A to B. The morphism itself will be denoted by 0, A to B, which is the composite of unique morphism A to 0 to B. Now, this 0 I am using to denote the zero object which is obviously a unique element. So, I can have a symbol for it. To take any A and B in that category, A to 0, there is a unique morphism and 0 to B, there is a unique morphism. Take the composite of this, that will be denoted by the zero morphism from A to B. So, 0, A, B. So, nobody told you this one, but it is there as now consequence of these axioms that such an element exists. These morphisms have the additional property that for any morphism F from D to A, G from B to E in C, we have if you pre-compose F with 0 A, B, it will be 0, 0 D, B. Similarly, if you post-compose G with 0 A, B, it will be 0 A, E. So, G is from B to E, whatever. So, they are all different zero morphisms, but composing with zero morphism any morphism, either this side or that side, right side or left side of a position 0. So, this conforms with our experience with zero morphisms of abelian groups, rings and so on, or vector spaces and so on. So, we will come back to initial object and treadmill object, but right now I will give you a construction now, because that is what my aim was in this lecture. So, pullbacks. We had introduced this one in part one in a very special circumstance, namely when you have a covering spaces or G covering spaces and so on and you have a map from any space into the bottom space, the base space. Then the covering could be pulled back onto the space X. Now, we would like to do the same kind of thing in any category, at least we do not know the existence and so on, but we will know that there is a concept like this. So, take any category, then fix a morphism from X to B. And a morphism from E to B. So, P is inside M E B and F is inside M X B. So, B is here the base for both the maps, B is the codome, that is the picture. Once you have fixed this, you will define another category itself now. In that category, which I am denoting by CFP. So, it depends upon the category C, where you are working. Then it depends upon F and P, which you have fixed, the two morphisms which you have fixed. So, CFP is a notation. So, this is going to be category, I have defined how. So, whose objects are commutative diagrams like this. Namely, F and P are fixed. Z is any other object, but then you have to take morphisms from Z to E as well as Z to X, such that this square is commutative. P composite alpha is equal to F composite beta. Take such things, they will be the objects of this category. Next I have defined what are the morphisms, verifying that the compositions and all that will be automatic because they depend upon the property of C being a category. So, what is a morphism from one such object to another object? So, I have to take two such squares. So, here Z1 alpha 1, Z1 beta 1, F and P are the same. Similarly, Z2 alpha 2 here, Z2 beta 2 there. So, this is one commutative square. That is another, this is the first one, that is another second one. A morphism will consist of now, a morphism from Z2 to Z1, one more extra area, all these things are given. So, a morphism from this square to that square consists of one morphism Z2 to Z1, gamma such that the entire thing is commutative. Namely, gamma followed by beta 1 is beta 2, gamma followed by alpha 1 is alpha 2. Then rest of them will be automatic. So, such a thing will be a morphism. If you have another Z3 and you have defined like this, then obviously, the compositor will be the compositor of gamma 1 and gamma 2 from previous case. Because we are using the category C, all that is obvious what we are going to do. So, this itself becomes a category. So, CFP is a category of diagrams of the squares. Now, a terminal object in this category will be called the pullback of P under F. So, a terminal object means it is some object like this, which will admit exactly one morphism from every other object. So, if Z1 satisfies that property, for every other Z2, there is only one more morphism like this, exactly one, not utmost one, remember that. So, then Z1 will be called the total space of this pullback. The pullback map itself will be this beta 1. The notation will be F star of P, fully P under F, F star of P. So, that is notation F star of P. So, the total space will be denoted by F star of P. The map to X will be denoted by projection map F star of P, whatever. By this, we mean the codomain of the morphism F star of P is X and whereas its domain is denoted by F star of P. The uniqueness of the pullback, you see this being a terminal object, the uniqueness of the pullback is obvious. Okay. So, in part one, we gave a constructive proof of the fact that in the category top, namely topological category, pullbacks exist. The same construction you can try in various other small categories, but they may fail to give you the full satisfactory answer that they may not be terminal objects in that sense. That part we have to verify, but quite often it may work. Okay. So, you see now because of this terminology, I have reduced the work of defining pullbacks, what I did for just the covering spaces. Okay. And prototype of that, I have defined it for umpteen number of cases, all categories, all morphisms. You construct a CFP in this way and look for the terminal object in that category. So, one single definition takes forever. So, this is the beauty of category for language. Okay. So, for example, recall that a category is called small category, if its objects, each object is a set. Like ENS is a small category. Top is a small category. Many of them rings, groups, they are all small categories because the object sets can be thought of as sets. They are subsets of subsets of the no, the underlying set is a subset of, can be thought of as a set. Okay. So, or you can say that they are in some sub-categories of edness. But that is not necessary. Small category just the object sets are sets, that is enough. Okay. Let A be any set. Okay. And consider category C A. Now, I am going to define another category, just another example. Whose objects are pairs A, G.  C is a category. I pick up A is any set and then I am taking A, G is a pair where G is an object in C. And A is a subset of G. For example, this category C could be topological category. Then G is an object means what? G is a topological space. But I can talk about subset of that, just a subset. A is A must be subset of that. Or this category may be a groups. Then every object is a group there. But then I can talk about a subset of that group. So, this A must be subset of that. Okay. So, take such pairs A, G, where G is an object in C and A is a subset of G. Now, these are the objects of this C A I am going to define. What are the morphisms? Morphisms are again commutative diagrams. See A to G1, I have this picture namely inclusion map. A to G2 also I have. And G1 and G2 are what? They are objects in this category. So, this F must be a morphism in this category such that these diagrams come out. Now, this thing makes sense because this is a set theoretic, it is a small category. So, you have to pass on to the subsets A to F composition as an ENS you have to do. Here also, this is some set inclusion. So, composition here is nothing but what? Composition in the small category, in the ENS. So, this diagram should come out and F must be a morphism in the given category. If you are taking topological category, this must be a continuous function. If you are taking groups, it must be a what? Homomorphism. If this is a category of vector spaces, this must be linear map and so on. So, this must be a morphism in that category. So, such diagrams will be called morphisms of this category. Objects are like inclusion maps like A to G1, the pairs of A, G is a super set of A or A is a subset of G. So, this is a category. In this category, take an initial object. If it exists, it is unique. If it may not exist, I do not know. If it exists, it is unique. That unique object, the initial object will be called free object in C with A as a basis. This is a definition. What is the meaning of free object in any category? Now, let us look at the examples that I am telling about namely groups or abelian groups or vector spaces or R models and so on. What happens to this? This should be nothing but free group, free abelian group, vector space or a free module over R with A as a basis. So, all these four different things we have studied very thoroughly at different places. All of them can be studied in one single go by this or express, right. Do not say it can be studied or express the ideas all about all of them in one single go. They are all free objects in a particular category, whatever category you are looking at. So, if you have proved a theorem for free objects, it will be true for all of them once in Galway. Construction could be also similar existence of constructions. I mean constructions for existence theorems but it may not work. So, you may have to keep modifying it. They are similar but you know always existence part you will have to use very special properties of the particular category that you are looking at, okay, that cannot be generalized. So, pullbacks etc are new but these free objects were somewhat old. I will ask you one simple question. If you take CDS topological spaces, what is the free object there? Think about it. So, direct limit and inverse limit is the next object that I want to discuss. So, go back to this example wherein we started with a partially ordered set and then converted into a category. So, that conversion was equivalent. You can recover it to get the partially ordered set. Namely, the category associated to a partially ordered set at objects are points of this set, members of this set. So, axis is set, okay. And morphisms are precisely one single element if filled only if axis less than or equal to y. If x and y are incomparable, MX y will be empty. So, that was the partially ordered set and that was the category that associated it, okay, right. So, we will use that now. We have seen how to view a poset as a smaller category. A directed set, okay, J comma instead of x comma something I have J comma less than or equal to is a poset such that for every two elements i and j, there is a k such that i is less than 2k and j is less than 2k. You know, i and j may not be comparable. If they are comparable, then I do not need another k there. One of them is bigger than that. But if they are not comparable, this is an extra assumption on the directed set. It is not a or it is not always true in a partially ordered set. Given any two elements, there is an element which is bigger than both of them. So, that is the meaning of it. There is a k such that i is less than 2k, j is less than 2k. Such a thing is called directed set. It is a partially ordered set with extra condition, okay. It is not difficult to reformulate this in terms of the category, corresponding category, okay. All that it means is given i and j inside j, there is a k such that M i k and M j k are non-empty. That is all. So, i less than 2k is if you are doing M i k is non-empty. j j k is non-empty, okay. You can talk about the same thing in slightly different language category. Now, a directed system I am going to define just as a covariant functor from this category. Now, this is your think of this as a category to any other category. If you have covariant functor, okay, taking values inside c, then this directed system is in the category c.  What are its constituents? For each element i in j in j, you would have an object here f j, right. And for each i less than or equal to j, there will be a morphism from f i, f j, f i to f j, right.  So, that is the picture of a directed set, directed system, okay. Associated to a directed system, we can define a category now, okay. See, like I started with with a and contain is a g and then a subset a, a set a and a category, then I define this category of pairs and so on, okay. So, c a I define. Similarly, fixing a map f and p, I define c, f p and so on. So, this game you have to keep playing. So, whatever you concept you have, first fix this category and look at the data to begin with and then out of that you have to construct the correct category. That category you look for initial or terminal objects according to your test. So, now what I am going to do? So, I am going to define another category which depends upon this system. The system if I, okay. So, I am just writing c f because it is taking value in c, just not to come to, neither c or nara, it depends upon c f. So, as follows. So, what is the objects first of all? The objects are the pairs here, first object here is a, a itself which is the category, in the category, then all these alpha j which are morphisms for each j and j. Where a is an object in c and alpha j's are all morphisms from f j to a. Remember f j's are given by this c f, okay. So, you have to have these morphisms, okay, such that alpha i is alpha j composed of f i j. Whenever f i j exists, f i j may not exist all the time, f i j is to exist only if i is less than or equal to j, remember that, okay. So, we can represent it by this kind of diagram here. For each pair i j wherein j is bigger than or equal to i, or i is less than or equal to j, you have a diagram. Diagram means what? This composite this, alpha j composite f i j is alpha i. So, this is your category now, this is your objects, okay. So, what are morphisms again? From one triangle like this to another triangle, you must have morphisms. So, morphisms are expressed like this, okay. Suppose you have a here and another on b here, for a you have all these f i's, f j is going into a and beta is coming into b. So, there must be a morphism in the category tau, let us say a to b is tau which fits all these diagrams for all j's and all betas alpha j's beta j's. So, one single tau should commute. So, that is a morphism. By the direct limit of the directed system f, with a direct limit now I am talking about, the directed system f, we mean an initial object in this category Cf, okay. Note that in general, the category Cf may be empty. Why you see, there is a lot of things you have to have, the category must have morphisms like this. For each i, this f i m of f i a is empty then there will not be any such thing, even if one of them is empty, there is nothing like that. So, there is lots of conditions here, okay. If this category itself may be empty, then there is no question of having an initial object, okay. Even if it is non-empty, there may not be initial object. If it exists, then only you say it is a directed, direct limit. Once it exists, it is unique, okay. So, a direct limit a, you mean an initial object in this category. We note that in general, the category Cf may be empty. If c has terminal objects, suppose I take a terminal object a, then automatically all these morphisms will be there and they will be communicative also because terminal object has this property. There is a unique map here. The composite has to be there, so their composite will be automatically this one, okay. So, it is non-empty at least. Terminal objects then, of course, this category is non-empty. However, there is still no guarantee that the direct limit will exist. Of course, an initial object exists, namely direct system. We have seen that this unit, okay. Then we can have some notation, direct limit of fj. Thus, the direct limit of a direct system in C is an object a in C together with the collection of morphisms alpha j from fj to a because it is after all it is an object in this new category that I have defined. Satisfying compatibility condition, this condition, okay, and then it must have these things, conditions are there. This must be also true, okay. Such that for every other compatible family beta j, there is a unique morphism from a to b, making the up diagram b. So, if it is an initial object, for every b which has satisfied this property, there must be a single tau. That is an initial object. So, this is the way, okay, a directed limit is defined every time whether it is a direct system of groups, direct system of topological spaces, direct system of rings, direct system of algebras and so on. So, all of them can be talked about in one single language. So, again, in the category sets itself, okay, every directed system has a direct limit. That may be due to the fact that there are lots of terminal objects there. Every single term is a terminal object. It may have some such, you know, impact on that, that why the direct system exists. I am not saying that is a proof or anything, okay. So, how do you do that? Take b to be the quotient of the disjoint union of Fj's. Now, Fj's are just sets. Take the disjoint union, then identify x with Fij of x whenever x is in Fy. Fy, there is a map from Fy to Fj. So, Fij of x should be identified with x itself. So, do this for all possible Fij's. Whenever x belongs to some Fj and there is amorphism further, you identify that map, identify this element with the image of that and so on, okay. That quotient set will satisfy the requirement. This being a quotient of all these automatically from each Fj there will be a map, okay, the quotient map. So, you will get a morphism whatever requirement is there. The same kind of construction, when I am same, it is not the same because you have to worry about the group operations and module operations, upper space operations and so on. But similar construction works in many other categories. These are all what are called as abelian categories or algebraic categories which are abelian, abelian categories. There are various terms, such terms which generalize many, many algebra, topology, analysis, computer science and all that together. So, that is the whole idea of of category theory. Perhaps we are coming to a close now, we will start talking about other things now, okay. So, let me just give you one more example. In top also, for example, this works, okay. What I have to do? Take disjoint union just like we did in the sets. Do the identification also. But what is the topology? On the disjoint union, take the disjoint union topology and on the quotient set, you take the quotient topology. So, that topology where you take direct system is a very special case namely it can be thought of as the co-induced topology, okay. So, many of these topological things that you have studied could have been worked in with category theory. On the other hand, topological ideas themselves will come back and generalize all this category theory, what are called as tapas. So, there are so many other things to do in the category theory. Very closely goes, in the beginning it looks like algebra but later on it becomes topology. In modern algebraic geometry, all these things are a must, we have to study all these things. So, for directed system, there is one small technical thing which helps, it has nothing to do with the category theory. So, it is better to know that since I am talking about directed system, I will tell you that namely suppose you have a sub-posset of a poset i, okay. So, this is a partially ordered set and this is some partially ordered set. We say this j is final in i, okay, it is called a final family usually in the terms but as a poset is suppose sub-posset is final in i, whenever for every i in i, you will have a j which will supersede that namely j is bigger than i. For example, if you take natural numbers for i and take only the odd integers here, odd natural number, this will be a sub-posset but it is final because given any natural number, there is an odd number which is bigger than that, it is like that, okay. It is like this is this concept is similar to subsequence, the concept of subsequence, okay. It is completely generalized like this, okay. You do not need to go to category theory, this is done even in the classically, okay.  If one of the direct limit exists, then both of them will exist and they will be equal, okay. So, this is, I said it is similar to subsequence. Now, for subsequence, we know subsequence limit may exist, sequence limit may not exist in general, right. So, there is a problem there, okay. But here, if for final family, if this exists, then this will also exist, okay. So, directed systems are already like Cauchy sequences, not just general sequences, that is why this works, okay. You can verify this one, this is just a remark. Finally, I said only directed system, I did not talk about inverse system. There is no need because all these things, all that you have to do is take C of namely reverse the arrows. Instead of covariant functor, take the contrivariant functor and do the same thing, what you get is the inverse system. And a terminal object will be a direct, is the inverse limit, okay. So, that is easy exercise for you to think about, okay. So, after that, I have a number of exercise here. You can keep trying them. Some of them we will discuss in assignments and so on. So, our next topic will be homology theory, that will be for another five weeks. Thank you.


Yota is a serial entrepreneur whose talent for developing effective ideas and solutions has resulted in successfully growing five companies with three successful exits. In 2012, Yota relocated to Silicon Valley and was an early investor in Bitcoin. Yota has worked with Nobel Prize-winning economists, the founder of the Jobs Act, a former SEC chairman, and the founder of ESA. Hey everyone, it's Rachel Wolfson here, senior reporter with Cointelegraph. Thanks again for joining us for a very special AMA Today. Today I'm joined with Yota Regev. He is the CEO slash CTO of Quantum Finance. Hey Yota, how's it going? Hey, Rachel, good to be here. Thank you very much for having me. Yeah. Thanks again for joining us. Before we get started, I want to remind the audience to please ask your questions in the chat. Yota is here to answer those. Yeah, without further ado, Yota, let's just get started with the AMA. First question that I want to ask you is, why do crypto projects have a high failure rate with the inability to scale even if sufficient funds are raised? Oh wow, it's very straightforward based on the history of the startup industry. I will give you some income from what's going on in the past so we can understand what will look like the future. So in the startup industry, 95% of startups fail, right? They're doing C, they're doing kind of pre-A, they're doing A, they're doing multiply round and they're still failing, right? And when it's come to a crypto project, the situation is very hard, even harder than a startup because if you remember, sorry, 2017, people used to raise best on napkin, right? White paper, hundreds of thousands, oh yeah, hundreds of mills of dollars. And then on 2019, there is tens of mills of dollars, but then investors want to see more a prototype, right? In 2021, project raised millions of dollars, but then investors want to see not just a prototype but also want to see some community around that prototype. Probably we're going to see project raising hundreds of thousands of dollars, but then investors probably will want to see a proof of success, they will want to see income stream, they will want to see some tier one VPC on board, stuff like that, that in other words, it's looked like the demand what startup need to perform before getting money is become to be more and more like the startup industry, but how much money is getting, you also start to look. So it's a big issue for a project because after it's doing a pre-launch, you cannot go after six months or let it go on the market. You cannot say, hey, my token is trading, let's conduct another 50% discount in order to raise another money. So in other words, it could be a great team, it could be a great idea, but the idea that the project cannot keep the light on, it cannot keep pressing money, it can put them out of business. That being said, there is another issue, when projects start and raise money, then the next step they invite exit strategy for the investors. So if there is no equity and the investor give up on the possibility to see any kind of liquidity in the near future, they start to dump the token even below the price that they purchased the token at just to get out, and that can bring the token into a position that it cannot recover from. And on top of everything that I just said, there is one more thing that is very important, real estate market, stock market, crypto market, they're very alike, they're all going to have cycles, bear market, bull market, bear market, bull market. It's going to stay here and it's part of the game and it's supposed to be like that, but what is not supposed to be like that is why projects that burn in 2017 died before 19? Why those that have been burned in 19 die before 21? I mean, how many died during that going div into the bear and never recover up from that? And that's the big issue that we facing. Everybody helping projects to go into the market. Nobody helped them to stay in the market. Right. Yeah. Great explanation. Um, let's talk a little bit about the bear market and how the impact crypto projects today. Do you think that crypto projects that are trying to raise funds or build within the bear market are doing anything wrong that may be impacting their success? Oh yeah, absolutely. I think, I think, uh, since, um, projects that have a lot of team token, treasury token, they cannot conduct another pre-sell. Uh, so the only thing that everybody is doing, but absolutely everybody. Um, and it's a big, big note to do that. Everybody doing the same thing, which is called stacking. Now what is stacking? Let, let's face it.  And I will give you a little bit more free tokens. So after the stacking will be over, you and your friends who will rest to the bottom, who is dumping first. Let me just give you more ammo so you can shoot me down even faster. Right. I think there was a senator, uh, in United States, they used to say back then that if you find yourself in a hole, stop digging. And I think the only thing that project have to do right now is try to do stacking in order to reduce cell pressure. But what they're really doing is just kicking the can down the road for future day, and then it will come like a big boomerun. Does that make sense? I know. I mean, that, that makes perfect sense. I love how candid you are about it. Yota, clearly you're very passionate about this. But no, I mean, it definitely, you know, it needs to be said because we are seeing this right now. Um, but let's talk a little bit about what a decent model involves and how that's different than a launch pad. Yeah. So basically, like I said before, everybody tried to help project to go into the market. So the word launchpad is well known. Everybody, you know, ICO, IDEO, anything that starts with I standing for initial offering, right? But nobody's helping project to stay in the market. And that's where basically scale pad is coming in, right? So scale pad is standing for how to take a project that is in the market, which doesn't matter if it's in the market for one day, one hour, a lot of liquidity, a little bit of equity. As long as it's in the market, it's good to go. And the next step after the launchpad is basically to create PDO, which is standing for post-dext offering. I can even share my screen for a second just to show here. Can you see my screen? Rachel, Rachel, can you, can you hear me? I can hear you. Nope. Oh, okay. So the post-dext offering is basically standing for a post and not initial and it's designed for existing project. Like I said, after the launchpad, after they already launched somewhere. And the main idea, if I'm going here into the platform, the main idea is that every person, every project that have a token, team token, treasury token, and actually not just a project, actually every person, because if you're a real investor and you have a lot of token or you're a developer and you have a lot of token, even an advisor that have a lot of token and you don't want to dump into the market, you don't want to hurt the project. You can utilize the PDO in order to find a way for exit. And I want to explain you how it works. So it will be kind of a clear idea of what's so cool about it. So the way that the PDO works is that you open a PDO and you offer for people to buy directly the token from you instead of going to Pancake Soap, Sushi Soap, any kind of dex. By the way, PDO is not a dex. It's a layer on top of any dex that is out there, even if it's a brand new. It's not a dex, it's a layer on top of that. So if you have, for example, some kind of a project, all right, let me look in just to demonstrate that. If you have a project and you want to basically find a way how to increase liquidity, how to increase the token value and how to raise money as you go, right? Basically what you need to do, you need to come to the PDO and I will show you example how it's looked like. So I want to open a PDO. I will take a token as an example. One of, let me choose a token that I have a pilot here to show you. Let's take a bakery, right? So let's take the smart contract for bakery. I will go to Coingeco, I will pull the bakery.  And then the way that it works, I put the smart contract address and then I choose the text that I want. I can choose if I want to basically create PDO based on fixed sale or doge sale and I can basically run the PDO all year long as many years as I want. There is no limitation. It's not like IDO, ICO that you have few days, few weeks with fixed price and then when it's going to the market and start to trade here, the price basically coming. I will choose this date and the price coming from the market basically directly from the pool. So every time the pool go up, go down, it's displaying the same price, so basically it's followed with the market. And then I can even do building, stacking, for example, instead of doing buy my token and then go to stack it, I can combine them two and I can do 365 days or I can do even 30 days or 60 days instead of offering 10% or 50% I can even offer 180 over 30 days, which is exactly 50% like one year. And I can do other features and then I can choose what to do with the procedure coming in. I can choose to take it to the liquidity pool. I can choose it to buy back tokens for early investor from the damper shield, which is another project that we have. If we have a time, we'll talk about it or I can do cash out, for example, 1.5%. In that case, I will choose, let's say, the cash out just to show example, how it's look like. And once I deploy the PDO, what will happen? Pay attention that I didn't put a logo. I didn't say how much the token works. I didn't say anything. I just basically come with my token and open a PDO because it's completely decentralized. It's not allowed to any person to basically add information. And once you have the PDO here, you see it's live and I can see all the information about the PDO. I can see what's the offering. If I want to check the project, what is all about even though it's already live? So I'm supposed to know that project. It's not about to go live. It's already live. I can go and check White Paper and I can check website and I can check even how much liquidity this project have right now in the market. So all the information is in front of me.  What's going on here? Why it's so unique and so different and it so can change the game? Because if somebody have poached out there and it's live on Pankaswap, SushiSwap, any kind of decks that means that most likely every day the project have buy pressure and sell pressure. You have to have both. Obviously during bear market, you have more sell pressure than buy and the other way around during the bull market. But every day you have to have both. Otherwise the price will go all the way up or all the way down. Now, I will give you an example. If somebody go to buy this bakery from Pankaswap. Let's say I go to Pankaswap and I want to buy this back token. So let's choose. Here we go. That's the back token and let's put for a second door so it will be easy to understand. So if I want to buy this token, let's say I want to deploy $10,000. Pay attention. How many tokens I will receive? I will receive $26,370, right? But look, the price in the market is $3,700. So I'm losing when I buying from Dexas and that's because of the slippage. Every project that have pools and user come to the pool to buy the token, they're losing for the slippage. Not only that, look what will happen if I will push $10,000 to this pool on Pankaswap. 36% price impact. You know what that means, Rachel? It means that the community and the project will not going to enjoy for my $10,000. That means that some boat going to do fund running because there's 36% price impact and it's going to steal the money. So when people buying the losing and the community losing because it's not really appreciating the price, it's just been stolen again and again and again by boats. Right? And the main idea is that if I want to buy the token from the project directly, I can come and buy from the project, from the video. So in other words, it's like hijacking all the traffic from all the Dexas. I don't really creating people to buy. They're already about to buy. Somebody is already about to go to Pankaswap to buy. So why to buy from Pankaswap and not buy directly from the project, right? When you buy from the project and you inject your money, you will get for your $10,000, you will get the same price. There will be no slippage. And 100% of that money will be injected to the pool with no fund running attack, which means it's going to increase the value of the pool. Like 50% will increase the value of the pool and the other 50 will be used to increase liquidity. And guess what, Rachel? The liquidity, the LP will be given to the project, not immediately, 30 days after the stake-in will be over. So there will be no front, no ramp pulling. But in other words, the project will have a sustainable liquidity. It will own its own liquidity. So it doesn't make sense to buy directly from Dexas token if the project offering from you to buy. Now, I will show you an example how let me choose a project here. I will show you if I'm investing in the project, what happened to the project, right? Let's pick a project. Let's say I go into this project, okay? I will put money in and I want to show you what will happen. So they have 100% go to the liquidity pool, right? So look over here on this project and let's choose, right? So you can see over here that is right now 2504, do you see that price? 254, do you see that? Now, let's say I want to put money in, right? So let's say I want to put, let me put 100, which is a small change, right? Just to show you how the price change in real time, right? So if I'm pushing that money to buy, first I will not have a slippage, but then what will happen in real time, the price will increase, the money will go to the pool, increase the pool, create liquidity, will boost the project. So me as a user, I'm benefiting, no slippage, the community enjoying from price appreciation and the project enjoying from basically more liquidity. Everybody win-win from that situation, right? So I will show you here in a second how the price increase instead of 0.254 we'll see what will happen. Boom, you see, it's increased and then it's going even higher, you see? So that's what's happened. Every time, instead of doing stacking, you're coming over here and you're doing building stacking that benefits you and everybody and it's better than the current stacking in the market. Got it. Yeah, that's a great presentation. Thank you. Sure, the audience, I just want to remind you guys if you guys have questions, please send them our way. It's really interesting projects that I look out for questions. Are projects already utilizing this model? Say it again, you're breaking up. Are projects already utilizing this model? Are they already participating in this PDF? Yeah, there is some projects that start together. We just right now doing a soft launch. The soft launch is right now, as we speak and in the next few days, we will do a hard launch but right now project is still coming in and basically open, it's free. You can open basically your PDO. You only basically pay percentage based on how much you sell. So it's performance-based. If nothing happened, you don't pay anything and it's available for every person, project, investor, developer, anybody that have token and it doesn't want to lose to the token or it doesn't want to lose to the market or it doesn't want to hurt its own project. It can utilize the PDO to keep increasing the liquidity, the token market and also raising at the same time some money into the team to keep the light on. Yeah, was it intentional for you to do this launch, the soft launch during the bear market?  It's very interesting question because I love the bear market because the bear market basically is like a desert. Nobody wants to play ball, everybody gets hurt and the desperate to get water, right? Everybody needs help. And if you're building a project that is all about helping and what is better time than actually the bear market to helping project. And I want to show you why users, investor, should basically invest in another project during the bear market using the PDO. I want to show you something that is designed based on quantum finance model, which is a very brand new concept that we bring into the blockchain. It's never been done before. So if you can see my screen, do you see here something called Secure Future? You see that link? So Secure Future is amazing because what is Secure Future? Secure Future basically said to you, listen, instead of go and injecting real time your money into the pool and get this API that this project is offering right here right now and the money will increase the value right here right now in the pool. Instead of that, if you have second thought, if you don't think that it's the right moment to invest in the project, maybe the market is not the right timing. So you can come to the Secure Future and you can basically put your money here, right? For example, you can put it here and what will happen is that your money will not be inject to the PDO, it will not inject to the pool. What will happen, it will go to work, it will go to compile it, it will go to inference, it will go to Venus, which is exactly the same place that you send your money to work during a bear market, right? You want to get as much as best API that exists with the low risk that is possible. So instead of sending your money again, we hide that net again. So instead of sending that to Venus, you basically send it to Venus through the PDO, through the Secure Future, so your money is over there. I can show you here that if you basically want to see the transaction, you can see that even though I invest to the PDO, my money is in Venus right now, right? And what that mean? That mean that I'm simultaneously, simultaneously holding to position I invest in the project, but I didn't invest in the project and I can change my mind and make the final decision in future date. In other words, Rachel, imagine yourself that someone said to you, listen, there is some guy called Zuckerberg, very crazy guy, he want to raise a lot of money and you have crazy idea to build something called social media online, but you don't have to put your money in play, you don't have to risk it. You can put it on the bank, get return and we'll keep the ticket for you. And if in the future we'll become to be a unicorn, we'll let you to collect that ticket like you invest in the ground floor. So the secure future, which is best on quantum finance model, it'll allow you to invest without investing, it'll allow you to keep the ticket, keep the EPY, keep the reward, but on the same time, stack your money in safe place that you put it anyway. And in future date, before the PDO is running out, before the time is kicking in, you can basically say, do I want to stay with Venus and take the EPY from whatever they're offering over there? Or I want to collect this winner ticket, the lottery ticket. I want to go after this project. So in other words, if there is people that thinking the Dutch coin is going to be whole around in the next bull run and they want to buy into the deep right now, they can basically use secure future to buy their forever token. And if they change the mind, they can still stack with Venus and compound. And if it's booming, they can jump back on the lottery ticket and collect that basically a grand floor position. It's never been done before. Nobody brought into the blockchain quantum finance solution that allow you to hold two position on the same time, like investing without invest. Mm-hmm. Yeah, it's super exciting. Audience, just to remind you there's a question. It is a really, really, really interesting question. So I want to ask you about the challenges in terms of smart contract vulnerabilities or issues because you've seen a lot of acts and scams and things happening to projects today. So Yota, what are your thoughts on that just with the safety of the platform? So let me tell you stuff about what... I know that not everybody is technical person, but I want to put some ground rule for everybody to understand. If somebody building a smart contract, regardless to us, everybody, any project out there, and you have privilege owner, right? Like the owner have the right to upgrade the smart contract, the now have right to upgrade the smart contract. That's mean that there is a door for someone to do something. Now, first thing that I could do is see if somebody have privilege and then you try to see how can I get into that door? How can I sneak in? Now, if you don't have a door, let's say Uniswap build a smart contract that is not a regrettable, which means nobody have the right to change that, not even Uniswap. If they want to change that, they need to relaunch a new smart contract and ask everybody to withdraw all the liquidity and move it to a new one. So if you want safe protocol to invest in, do not invest in protocol that have basically a credible position because maybe you don't have the knowledge to understand where the back door is and how safe it is. So it's better to go first thing first after protocol that they're not a credible, so they're basically more secure and PDO is not a credible. Got it, okay. Also, let's switch back, Yoda. I can't see your face. I can only see your screen share because I'm gonna take a question from the audience and it would be good to see, okay, there you are, hey. Okay, so go positive is asking, how can we invest in PDO finance does that, I don't know if they're talking about the platform itself or just the projects on the platform, Yoda, do you know? Let me answer both. So if somebody want to invest in project that's on the pad, you just need to come to the PDO and invest in the pad. And if that person thinking that you know other project and you want to invite them in, it can go to the PDO, I will quickly share again my screen, you can go to the PDO and basically connect his wallet and generate a unique affiliate. So it will allow him to invite people, invite project people to open a PDO and then he will get rewarded every time that basically working and generate income, he will basically get rewarded for that. Another option is apply for licensing. So we are B2B, we are infrastructure company, we're building stuff as infrastructure. So basically our main model is basically to allow people or qualified partners to have their own PDO. They can call it whatever they want with their own color by few click, they can design it as much as they like, they can even collect any fees that they want. And we have a lot of partners that already lined up. For example, we have DEX tools that they have six to 12 million user a day apply to get the licensing for the PDO and other partners. So the main idea if somebody want to utilize the PDO, the scale pad in order to turn it into an income stream, it can be an affiliate or can be a licensing fee. Now, if somebody want to invest in the project, our project, basically we used to have a pre-sell only for existing investors. We didn't want to open that for new investors, but we may consider if it's a good partner with added value, but that being said, we will do some public offering done the road which is comply with the regulation with a new concept called IBO. We'll do a different session AMA on the IBO because it's blowing my brand new concept and it will allow people to invest in project in a new way that is compliant with regulation. It's not a security and the risk been removed. And we will obviously open a PDO for own PDO. So soon there will be PDO for on token PDO and people can even buy directly on the ground floor with or without the secure future that I mentioned. Got it, okay. I also wanted to ask you about how does PDO ensure that discount tokens are not dumped? And I know that we've got a screen share to show the Dumpershield UI. Yodi, do you want to elaborate on that while we also pull that screen share up? Sure, sure, sure, I will even share my screen again. So Dumpershield is another technology that we created on quantum finance. And it's very interesting technology because it's also containing a quantum finance solution based on game theory, like the prison dilemma theory. I will quickly explain you what that means. When today project doing airdrop or presale or public sale or anything that end up with discount token, usually they want to lock those tokens from some period of time, right? Like longer time, shorter time. And then what happened is that usually it's end up very badly for everybody, right? Everything is tanking. Now, why is that? And the reason for that or the answer for that is because what is called the prison dilemma. The prison dilemma is a game theory that says that if I'm going after vesting and you're going after vesting and let's say after 12 months or six months or 30 days we both supposed to release to the market, right? It will be available to sell our token. I'm thinking to myself and you do the same, should I hold because I think somebody else will hold so it's benefit the project and everybody will enjoy from or should I dump because I think you're a mean person and you're going to dump before me on me. So I should be quickly finger going and dump before you. And you know how it's end up all the time, right? It's like rest to the bottom, right? And that's the ugly story of every vesting that exists out there today. That being said, imagine yourself a new word that you can basically put vesting without vesting, right? You basically can engage with liquidity during the vesting time. And what's cool about it, not only that there is basically decentralized seed that allow people to basically go ahead and sell the tokens to other people without even even if they don't know them but imagine to yourself, I can not show it right here right now because it's coming soon but imagine to yourself that there is a something called gateway and the gateway, this is the gateway. So the brilliant everything about the damper shield gateway basically set you if you have a token and you're behind the damper shield, let's say for 12 months, you don't have to wait 12 months for the gate to be open. You can basically engage with liquidity during the vesting time. So hopefully by the end of the vesting time the sell pressure will be reduced or maybe there will be no sell pressure anymore. And I will quickly explain you how it works. So imagine to yourself that me and you behind the damper shield and we both want to sell our token. So we're coming to the gateway, we say, we want to sell, you say, I want to sell. And what really happened is that me and you need to vote how much discount we're willing to give to a buyer. Let's say we agree to give to a buyer 10% discount below whatever the market is, right? So what that means that every person can come into the gateway, deposit native token or stablecoin and buy our token with 10% discount. And then you can go to Uniswap, Bank of Swap, Binance, wherever the token is trade and sell it over there immediately. And whatever leftover that you couldn't sell it can return back to the smart project and get his money back. So first thing for that buyer, it doesn't have a risk because it can get the money back and doesn't have a risk, right? But the gateway is very smart. It will not allow me to sell as much as we want and give buyer the privilege to buy as much as you want. You're basically going to check every day how much the appreciation of our token was versus yesterday. So if we have let's say token worth one dollar and from yesterday to today, it's increased to by 10 cent. Let's say dollar 10. So that's mean the gateway will allow people to buy token with discount in a way that they can only dump the market by 50% of yesterday appreciation, which mean to dollar zero five. So every day it will check how much appreciation being incurred and it will allow a little bit dumping to take place every day, but the graph will keep going up and up and up for until the end of the vesting time. So in other words, you're engaging with liquidity but you don't dumping the price as you do it every day. And by the end of the vesting, maybe you don't need to engage with liquidity anymore. Everything maybe you even want to buy more because everything's so boomed. Right, yeah. Super interesting stuff. We're actually running out of time. So Yoda, my last question for you is what can we expect next from Quantum Finance? Wow, we have so exciting stuff that we're about to bring into the market. Some of them will be Q4, some of them will be Q1 next year. So for example, we're going to introduce first-of-the-kind insurance for LPs from dumping. Can you imagine yourself? Everybody know that if you have insurance, you cannot protect something that's about to happen. So you cannot ensure that there will be no sun tomorrow because we know that there will be a sun in the sky tomorrow. So nobody can ensure you that there will be no dumping because we know that the market go up and down every time so there will be dumping no matter what. But imagine yourself that it could be decentralized insurance to protect LP from dumping, right? So that's really blowing my mind. And on top of that, there will be a technology that we will introduce that allow people to buy Metaverse land and basically NFTs and music and game, but without ability to be exposed for downside. Imagine that you can blindly go and buy whatever the heck is out there, but without the exposure of the downside. That's never been seen before. Everybody said to you, if you put your money to work, you need to take under consideration that you say bye-bye to the money first because there is a risk to lose it, everything. But what if quantum finance can allow you to basically remove the risk and not engage with any kind of a downside, right? Or imagine yourself a scenario that you can invest in any crypto market project or imagine the crypto project, no matter who they are, without discrimination, without checking the white paper, without checking the team, without try to understand who they are. Imagine yourself that they can raise money by click of a button, right? Anytime, even during a bear market. And those investors that invest, imagine to yourself that they don't have exposure for any loss, right? So I know that what I'm saying right now, it doesn't make sense how it can happen, how those stuff can play when we know for sure that investment in vaulting risk and there is nothing free and risk is always there. But again, I want to remind you that until today, everybody built technologies and smart and track with the logic of binary code, right? A one in zero, true and false. Nobody ever built any technology and bought it into the blockchain with quantum finance model that allow you to basically hold multiple position and invest without investing or see the future first and make decision later, right? So the stuff that we bring going to blow minds and again, it's either going to be worth nothing and it's going to change nothing or it's going to change everything. Everybody that going later on will say that was fun and it's never going to go back again after that. Yeah, exactly. Well, hopefully this is going to change a lot and I'm looking forward to our next AMA and I'm looking forward to hearing more about quantum finance when the time comes. We're actually out of time now. So I just want to thank the audience again for joining us. Thanks for your questions. Just a reminder to subscribe to our AMA channel. We do these to our YouTube channel. Sorry, we do these AMAs all the time. Yoda, it's been a real pleasure. Thank you again for joining us. Did you want to say anything before we sign off Yoda to the audience? Maybe how to get in touch with you or is there a Twitter? Yeah, I mean, if somebody wants to get in touch with us we have social media but they can also look me up on LinkedIn. And yeah, and maybe the first will be with you. Yeah, awesome. Cool, thanks again guys. Thanks everyone for joining us and we'll see you next time. Bye. Cheers, bye-bye.


to work or not to work. Today I'm going to take a look at employment versus entrepreneurship. And the question I'm asking today is which of the two can we call a more sustainable tool for economic development? I'm taking a total deviation from all we're talking about, but it's interesting that we're still talking finances, but we're now looking at the bigger picture. So what do you do for a living?  I'm an entrepreneur, seems to be the buzz phrase on everyone's lips. Well, it is no surprise as the rate at which people are starting their own businesses and opening retail outlets has astronomically increased in the recent past. May I at this juncture put a disclaimer? I am no economist. I'm not an accountant like a gemai. I don't have a financial interest in a book like Citi and I'm not doing agreements and co. I'm just a lawyer who has delved into development and I have a fascination for building human lives. Now let's take a look at the definition of employment. Employment is defined as a state of having paid work while entrepreneurship is referred to as a creation or extraction of value. In recent times, especially in Nigeria, they have been various discussions around entrepreneurship as a tool for growth and sustainable economic development. And it's interesting that the last time we're here together, it might actually made a very strong case for entrepreneurship as a tool for development. And so it's interesting that we're here again talking about this today. Now let's actually take a look at this debate on whether entrepreneurship or employment is the answer. A 2019 World Bank report states that Nigeria could enable millions of citizens to escape poverty over the next decade through enacting bold reforms designed to boost economic productivity. Without robust productivity growth, the report wants that living standards will continue to deteriorate and the number of people living in poverty will continue to rise, increasing by more than 30 million by 2030. And unless the pace of growth and job creation accelerates, the forecast is gloom. As Nigeria's population is expected to grow by as much as 35 million in the next decade, meaning that Nigeria as a country will account for a quarter of all people living in extreme poverty worldwide. A salient point, however, is that economists are saying that creating new opportunities for this rapidly increasing labor force will require a new economic model based on productivity growth. In that same report, the report then went ahead to outline four priority areas that could help lay the foundation for Nigeria's transition to a new economic model that makes more effective use of its young population and abundant resources as a way to support sustainable growth and poverty reduction. So it is interesting that Ejimei has written financial literacy books for children and that it here has decided to help all of us come out of poverty by having a book of financial literacy. It could never have come at a more apt time. So the first thing that the report mentioned was to ensure policy transparency and predictability. And this is critical in reducing investment risk for people that are taking investment and promoting growth. Secondly, would be to enhance factor quality in various areas, such as investment infrastructure, which we know is direly needed in Nigeria today, improving educational outcomes, liberalizing the trade regime, and other factors that would help develop value chains that facilitate the efficient reallocation of factors of production, thereby making Nigeria a more cost competitive economy. But then I don't know with the kind of news that we're hearing today now where BDCs are being regulated, I don't know if that advice may not need to come in again. However, thirdly, they need to regulate to reduce regulated discretion in order to help attract foreign and domestic investment and encourage competition. And fourthly, the report says that there's a need to improve access to finance. But in all that has been said in the report, in all that I have gone on about, for Emeka, for Shade, for Aki, Haruno, and even for Ida with her post-noctal agreement, the reality is that we probably all need a blend of the daring risk-taking entrepreneurs and an integral part of the factors of production, which is labor or employment, as the activity itself is actually called. Because labor is indeed the factor that starts production. And although it is alluded to that no country can grow without having citizens that are daring, if we all become entrepreneurs, then who carries out the work that the entrepreneur is creating? Yes, I know. I simplify the matter. But alas, I am only making a case for a blended view to sustainable economic development. And more importantly, for the personal economic plan that we all as Nigerians have to deal with. So once again, my question would be to work or not to work for yourself or for somebody. And I say we all work whether as entrepreneurs or as employees. Well, unfortunately, you know, applying, you have the possibility or the probability of having less employees. You know, I've said this thing before and I will say it again. Why do you have room for less employees? It's obvious. We don't produce anything. I was in trade fair on Monday. I decided to break the jinx and go look around and see what all the boss is. And as I was driving into this massive, one of the biggest markets in West Africa, worldly out and all that. But the striking thing is that they are all selling and not producing. What we need to do to create the employee, like Anita mentioned, is to have the back chain of the end product. To have people producing what we are selling. It's not enough to just put the trailers on the high sea and land them and crowd a papa. Yeah. I was wondering how come Lagos is so crowded and why there is always traffic.  What is going on? Very simple. New York is crowded. Of course, London's on one to four is crowded. But what the government have done is that they've decentralized the economy. You don't have to come to Lagos for you to make a living. But here, we all have to come to Lagos to buy ourselves. You don't even all have to come to Lagos to buy and sell. Before COVID-19, we all had to come to VI to work. To work. It didn't make any sense. Everybody. Everybody that's going to work in the morning is driving from this point and this point to VI. Every bank head office has to be in VI. Every company's head office has. Even the law, it's left in the mainland to go to the VI. No, I agree with you. It is crowded. But you see the question and what I'm seeing and I think is this.  Or boss lady, boss boss. It's just society just being silly. I see young people don't want to work. Three cultures of the people who say, oh I want to be an entrepreneur. I want to be an intellectuals lazy. They can't. They're not even employable. Come into my world and see what I see. When Rory said that lesion Idrians were all quick to crucify him. Oh, in this my business, like I said me now, I fall into below both employee and entrepreneur. This is my entrepreneurship journey. The greatest problem I have are dedicated staff. We need to get to the job before the job starts. God forbid they resume at eight. They will literally fall down and die. And that's why I had to ask the question and really look at it and say to ourselves that before the next generation and sadly you know really really before they get so lost and so carried away not realizing that even the process of entrepreneurship itself is not I just jump into it. The skills that you require, the abilities you need. To say this all the time I say if you haven't worked in corporate Nigeria and then you just want to jump into entrepreneurship you're going to fail at whatever you want. Because you won't even know how to do a report. You won't know how to get accountable to anybody. You think that oh I just wake up and resume at eight. They never know how to sell the product to people. Somebody says I'm selling something and I'm like okay you know what tell me about it and I hear I have it. I'm thinking isn't it difficult for you to actually analyze and itemize what this thing does and sell me on it. I'm not saying marketable. Come across like you actually understand what your business is about. It's zilch. So that was really what pushed this this question today for me. We were actually at an event yesterday. We were selling the books and I was at the event. My staff was there and they were distributing snacks and party packs and everything. So I saw his party pack there and of course there was a donut in his hand and he was chewing the donuts and there was our market that I was supposed to sell. I just said guy put down your donuts. I said I don't understand. So I don't know. I don't know. Maybe Titi has a different opinion. I don't know. I don't have a different opinion.  You do trip inings and things like that. You definitely would have a lot of glitches along the way. I've seen a lot of businesses that even though they know what it is they are doing but the processes are just wrong and that's obviously at the end of the day affects the turn out of the business. So obviously it is very important to have gone through the corporate world and understand how things are done day to day.  Well, I think in all in all really when Titi Bilala was talking that was the part she mentioned about discipline. I think that's the one thing that maybe might be saving grace. But before we go on the issues of food insecurity discussed last week Kaewan Webster says the government needs to help their people. We have now come to the end of this week's episode of The Advocates very sadly. However, The Advocacy continues on our social media platforms on Facebook plus TV Africa hashtag the advocate NG or on Instagram at plus TV Africa hashtag the advocate NG. To catch up with previous broadcasts go to plus TV Africa dot com forward slash advocate NG and don't forget to subscribe to our YouTube channel plus TV Africa till next week. It's same time on this station. Let's keep advocating for a better society. Bye. Bye.


The Derby Festival. They say the Derby Festival is but it runs for a whole week so we only go for three days so it's official. This is the number one festival in Kentucky so welcome to the number one festival in Kentucky. It's because of hillbilly days in Pikeville that we can take care of every child that comes through our door. If they don't have insurance we say so what? If they have inadequate insurance we say so what?