Categories, Sites et Champs - lecture 1 of 3 — Part 4

0:00 Equalization. So, in a topological space, there is not all the arrows with inclusions. All the arrows with inclusions are the ones that lead to the truth. It's non-linear. And since there are two objects, there is a third which is linear. So here, there is the... the morphism... the morphism of a system, which is the inclusions. And, you see, hop, it's the inclusions in the form. So, at some point, two... If u0 is 1, then u0 is u1, and if u0 is u1, then u0 is u1, and if u0 is u1, then u0 is u1, and if u0 is u1, then u0 is u1, and if u0 is u1, then u0 is u1, and if u0 is u1, then u0 is u1, and if u0 is u1, then u0 is u1, and if u0 is u1, then u0 is u1, and if u0 is u1, then u0 is u1, and if u0 is u1, then u0 is u1, and if u0 is u1, then u0 is u1, and if u0 is u1, then u0 is u1, and if u0 is u1, then u0 is u1, and if u0 is u1, then u0 is u1, and if u0 is u1, then u0 is u1, There is an exact transport, an exact transport, an exact transport. So, the counter is there. The counter, what is it called? It is in the middle of the counter, in the middle of the counter. It is in the middle of the counter, in the middle of the counter. So, this counter has two sides. This is the equation of the equation. The middle of the counter is an exact counter. The middle of the counter is an equation of the equation. The third function is here, it is obviously exact, it does not mean that it does not exist, as we have already done.

2:30 It is a function of direct image. We gave a name to it. The third function is here. It is a function of direct image. So, earlier, I was telling you a story. I told you a certain hypothesis. A star admits an adjoining to the other. And the other hypothesis, an adjoining to the right. If both hypotheses are correct, there is an airplane on the right and an airplane on the left, so it is exact. So I forgot to tell you that this is what an exact counter is. The theory of topology and geometry, there is a simple and a difficult part. The simple part is that when we have a model that the category is set, it adds products, well, not products, but objects, and fiber products. That's what the theory is. So we have two languages.

5:00 Thank you for watching this video. So I didn't say that C is a final object, but if C is a final object, I note, it's not too bad, since C is a final object, it's not too bad, since C is a final object, I note, it's not too bad, since C is a final object, it's not too bad, since C is a final object, it's not too bad, since C is a final object, it's not too bad, since C is a final object, it's not too bad, since C is a final object, it's not too bad, since C is a final object, it's not too bad, since C is a final object, it's not too bad, since C is a final object, it's not too bad, We know Higgs as a galerian, a very compact space, and we know that Higgs is relatively compact. Higgs is relatively compact. We know that Higgs belongs to a category, we know that Higgs belongs to a class, but Higgs does not belong, there is no decimal. So it is often the case that when we talk about a category, there is no decimal. Let's imagine a situation where an algebraic symbol, for example, is the same final object. And the final object has a straight line at the end of the line, a point. So if it's not in the category, it's still in the category.

7:30 Of course, another thing, in a category, if there is a final object, there is a point, a point C. The product used in the science is a product of this product or of this product or of this product of the science. There is no science, in fact, we know it. So, it's a bit clear, but it's still a product of the science. So, the idea of an academic lecture is a bit of a algebraic science because there are a lot of scientists who have a lot of problems and there is no universe. And to replace that with... to replace it with... Actually, there are people who say that. First of all, there are people who say that. That is to say that instead of taking an envelope, for example, in the front, we keep envelopes that are exactly the same as the envelopes. That is to say, the envelopes... I mean, it's not that I don't like the fact that there's nothing here. It's just that it's impossible. That is to say, the envelopes, for example, that... So, the idea of mathematics is to say that, you can first say that a plasticity is a contravariant, and then in the subject we can conclude that it is only a plasticity. So, I don't know the static theory of plasticity, I can directly say the non-plasticity theory of plasticity, but if you do not know the static theory of plasticity, the notion of plasticity is... To define a preceptor, we need numbers. To define what a preceptor is, we need numbers, numbers, and a solution. So, we have to come up with a solution afterwards, a solution. What does that mean? It means taking a solution after a solution. Look at what are the important properties of a solution and put them into action. That's the solution. So, a solution, in any case, it will be what is a solution of a solution. There will also be a certain family of facts, the Z-R-U, so there will be a part of the subject as if it were a subject in S, a subject in U, that is to say, an object in T-U.

10:00 Then there will be the subject, the S, and then in T-U. So it's a family of facts. So in the meantime, we use indexed locations, that is to say, exactly the same thing. For those who don't know, you can have two or three of the same unit, for example, a unit and a unit with the same, so the excess is not exactly the same, it's just a little bit more difficult to understand. So you have a part in there. So first I want to ask you a few questions. One of the elements of M is a phase, a V-virus, which is very often, for physicists, I would say, simply V, the rest. So there is a need to discover it. If you now have B in C, the fiber product of U is B, then you have B, and you have U, and you can even make family products, fiber products, you just have to think of them as intersections. If you don't have that, you have the ability to convert data into U. Excuse me, I'm going to show you what I'm doing. Ah, no, sorry. Yes, you have data into U, and then you have the ability to convert data into U. So, in terms of knowledge, you don't want to convert data into U. So, if you want to have two, but F1 and F2 are also in U, you can also convert F1 into U. F2, that's my 3. This is the first part of the second part. What you have invented here, you have found, I would say,

12:30 what you can define as things that are, that are, that are emotional in the first place. For the time being, all of these principles will be used in the future for the future. A topology, now pay attention because if you think about it, a topology in the past was the data of the open spaces. Now, the open spaces are fixed, because a topology is not the data of the open spaces, it is the data of the openings. That's it. So the opening is fixed, but the openings are not the same. All of this is part of a family of objects, which is a family of objects, of two parts, which have the same components.

15:00 With him, there is the object, he is really himself. I tell you, it's the same method, I tell you it's the same way. This is the first time I've seen this, this is the first time I've seen this, this is the first time I've seen this, this is the first time I've seen this, this is the first time I've seen this, this is the first time I've seen this, this is the

22:30 There's a lot of stuff. The theory of step by step. Anyway, we'll see, by the way.

25:00 There's a lot of bullshit. You'll find a whole week of bullshit. You'll find a whole week of bullshit by saying... by repeating the same things over and over again. I think it's... I think it's... I think it's... I think it's... I think it's... I think it's... I think it's... I think it's... I think it's... First of all, we need to know the type of particle, so if Y is the type of particle, it must be a particle of the same size as the one we are looking for. So we have to know the target of the particle, the target of the particle that we are looking for, and if Y is the target of the particle that we are looking for, we have to find out if Y is the target of the particle that we are looking for,

27:30 and if Y is the target of the particle that we are looking for, we have to find out if Y is the target of the particle that we are looking for.

30:00 And the most usual type of LRN, or LRN variety, which is very attractive to the audience. And there are many questions about it. For example, very often, in winter, we look at, for example, in February, the functions of the Trois-Francs and the Trois-Francs-Polynesians on the border. Often, we have a conversation about all the functions of the Trois-Francs and the Trois-Francs-Polynesians, but they are buried, etc. Well, if you really understand something, you lose, and you go back to the border. Thank you for your attention.