Categories, Sites et Champs - lecture 1 of 3 — Part 2

0:00 It is important to know the definition of the scientific literature of the A.B.N. to evaluate the modules on an anodic cycle of the A.B.N. This is an example. So, I think chapter 1 is stabilized. Chapter 2... Yes, chapter 1 and 2. And by the way, on the exam, I will tell you a little before, but first, you have the right to write your answers.

2:30 Then, the exam will focus on chapters 1, 2, 3, not on the questions. And then, chapter 3, which we are about to do, there are 13 chapters in total. So, to continue chapter 3, I will remind you of an argument that we have. So, I call it a specific principle. It is another categorical one. It is a specific principle. It is, on the other hand, an amortization of a specific principle. It's a morphing that goes in the other direction, so it's going to be F with a little p. I don't know what it's going to be, I don't have a good notation, so I don't know what it's going to be. Okay? Okay. Good. Then, a preceptor, the category of preceptors at the value of a category A. It's the category of spinners at the value of A. So there's nothing new. These are just some of the concepts, but with different approaches. That's why it's a little bit different. So, if we want to have an education, as I said before, we have an example, a topological space. The ICI is open in the X. For example, if you have continuous applications, it will be open in the Y, and open in the Y. There is a notation for PSH, PSH square, PSH equal to 1, and PSH equal to 100.

5:00 If you look at your notebook, there is a little change at the end. There is a definition of the two categories of additives and abelians, which is still in the process of being developed. If you are interested in the definition of the two categories of abelians, you will be able to follow it. The other important thing is that you will have the right to take the exam. And that the exam will focus on the three main chapters. In any case, at the exam, there will be at least two questions on the three main chapters. So chapters 1 and 2 are stabilized. Chapter 3, I'll tell you a little bit about it. It's not a problem, it's an error. But it's almost the same idea as we said in the beginning. So, chapter 3 is the precepts, as I said. Precepts are categories. A precept is a precept. It's a precept, it's a counter, but it's in the opposite direction. So, the precepts category, if you will, is the opposite of a category, of categories in a given universe. Notations, precepts are the countervariant factors, in their own way. Speakers include K-i, which is the value of a box of cards, so this is an example of an academic seminar. Speakers together include simply C-h-i. By definition, it is the same thing as what I just noted, hats. So you can see that C-i is the value of C-h-i. It's a bit weird, but we can consider it. For example, in a topological space, we can draw a universe as a trapezoid.

7:30 So, I repeat again, the model we must have in mind, not that we must have it in mind, it's not that we must have it in mind, is a topological space, each of which is covered. A morphing of a topological space, that is to say a trapezoid, you can see well that it has a different model, it has a different version. So, that's why it's very important. It's important to have topological spaces. For example, if you want to study a space, you can use the FDU assignments and if you want to continue, you can use the FDU assignments and if you want to continue, you can use the FDU assignments and the FDU assignments. I'm going to go too fast, I don't know if you can hear me, I'm going to go too fast, I don't know if you can hear me, I'm going to go too fast, I don't know if you can hear me, I'm going to go too fast, I don't know if you can hear me, I'm going to go too fast, I don't know if you can hear me, I'm going to go too fast, I don't know if you can hear me, I'm going to go too fast, I don't know if you can hear me, I'm going to go too fast, I don't know if you can hear me, I'm going to go too fast, I don't know if you can hear me, I'm going to go too fast, I don't know if you can hear me, I'm going to go too fast, I don't know if you can hear me, I'm going to go too fast, I don't know if you can hear me, I'm going to go too fast So, if you go down, you will find the set of set of set of set of set of set of set of set of set of set of set of set of set of set of set of That is to say, a counter to the value of A, as you can see, G composed with C, it goes from a counter of C to the value of A, and that's what we call a trigonometric equation.

10:00 That's what we call the equation G. So the equation is a counter to the value of A. However, what we have now is much more complicated. There are two theories, one on the right and the other on the left, on the right and on the left, on the left and on the right, on the right and on the left, on the left and on the left, on the right and on the left, on the right and on the left, on the left and on the left, on the right and on the left, on the left and on the left, on the right and on the left. So, it's true, I don't know if it's true or not, but I think that the people who are going to ask me will do an extension of Kahn. So, let's suppose, let's suppose, yes, we don't bother you, let's suppose that the list is small. The list is small. It's clear, we don't have to worry about the questions of the lecture. So, let's assume that A admits, admits, it's not that A admits, it's that A admits. D is the derivative, D is the derivative, D is the derivative. So, what do we do? We add an adjunct to the other. What do we do? We add an adjunct to the other. And if you have the names of A, it's the same.

12:30 If white people admit that they are positive, then white people have the right to say that they are positive. But that's not the way to do it, it's the other way around. So, first of all, I say that these two theories, these two theories are the same thing. They are the same thing. I don't know if they are the same. I don't know. In addition, it's really not good because you really have to do an exercise to find out what they are. Another exercise is to see if the two lectures are the same, in relation to the fact that they are the same, by the fact that they are the same, rather than the fact that one of them is the same. In relation to the fact that one of them is the same, it's not the same, it's the opposite, it's the opposite. All of these are the same. So, if you want to go from A to B, you have to go from A to B, you have to go from A to B, you have to go from A to B, you have to go from A to B, you have to go from A to B, you have to go from A to B, you have to go from A to B, you have to go from A to B, you have to go from A to B, you have to go from A to B, you have to go from A to B, you have to go from A to B, you have to go from A to B, you have to go from A to B, you have to go from A to B, you have to go from A to B, you have to go from A to B, What does it mean when you add a word? When you add a letter, you add a letter.

15:00 What does it mean when you add a letter? When you add a letter, you add a letter. When you add a letter, you add a letter. So, if you have S and A, then you have A. So, if you have S and A, then you have A. When you're doing maths, it's important to remember the alphabets, because it's a different kind of theory. Even if you have the same number of numbers, they're not the same. So, if you call S a series of series, G is a series of series of S. So, you can do that. It's not always possible, but it's still possible. So, to say that the counters are adjoined, to say that S1, S2 are a pair of counters adjoined, it means that we have an isomorphism like that, counterian, in ATG. So, if I replace A, sorry, because I don't have A, you see that C, H, Y, A, O, C, C, F, H, Y, A, O, that's right, that's the counter. Thank you for your attention.

17:30 In fact, nothing has changed. So, let's demonstrate the first one. So, I'm going to construct it. It's not just an interesting aspect. It's a construction. So, I'm going to give you a little... not too much effort. How is it defined? It's a 2G wave. So, I'm going to define it. This is going to be a sphere, a sphere-like sphere on Y. So, I'm going to tell you how big it is on an open sphere of Y. Imagine you are in topology. You have a As always in mathematics, when we introduce a problem, we take everything that can be used as a solution, and we put it in the objective or projective. So we have two candidates, and the candidates are quite a lot of them. You see, this is not, if I was in topology, F of U, this is not an open of Y. On the other hand, it may contain open ones, or it may contain open ones. Sure enough, there are all kinds of facts. So instead of taking the fact that it is not open, we will take all the things, all the openings that it contains, or all the openings that are contained. It is not the idea, it is behind what I am going to do. So for the limit of the field, we will take all the openings that contain F . So we take the limit of the field for F .

20:00 In other words, if you send an FD to a B, that's a good thing. That means that for all the Bs, they have... For all the Bs, this B is considered to be an FD. You can't talk about anything other than the green. So I'm not talking about FD, it doesn't make sense. However, at the same time, it's a form of an FD. It's a form of an FD. So you can either look at the 3D images that are contained in one, and there you will have the largest possible objective, which is the objective unit, or those that contain one, and you will have the objective unit. So I just gave you an example for DAGDAG. Under the hypothesis that there are objective units, it is quite the opposite. This is an objective unit for FT2D, which is contained in one. So you can see that it forms a kind of circle. And so on, and so on, and so on, and so on, and so on, and so on, and so on, and so on, and so on, and so on, and so on, For Euclid, Euclid, Euclid, Euclid, Euclid, Euclid, Euclid, Euclid, Euclid, Euclid, Euclid, Euclid, Euclid, Euclid, Euclid.

22:30 I'll show you how to do it. I take a arrow, and I take an arrow with an arrow pointing to the direction of the arrow. The arrow points to the direction of the arrow. And if I use an arrow, it points to the direction of the arrow. So if I use an arrow pointing to the direction of the arrow, I use an arrow pointing to the direction of the arrow. So the arrow points to the direction of the arrow. And now we take the additive light, which is this one here, and we take the effect of the additive light, which is this one here, and we take the additive light, which is this one here, and we take the additive light, which is this one here, and we take the additive light, which is this one here, and we take the additive light, which is this one here.

25:00 So, we have shown you, for the time being, we have simply shown you that FH2G, well, there were restrictions, and it's pretty obvious, and it's compatible, so it's well protected. So now, I'm going to show you the form of the induction, so it's the same kind of calculations. It's a bit difficult because there are passages in the course where you have to understand what is being said. So it's a whole passage where we have all the formulas, we have to go through the threads, so if we don't understand anything, it's not easy, and then we have to go through all of them. There, we have to go through all of them. So I'm going to go through the formula that's there. So I'm going to construct, I'm going to construct lines in the two terms. In the same way as in the notes, I thought of the applications, not the pieces, I thought of the objects, I thought of the objects, I thought of the objects, I thought of the objects, I thought of the objects, I thought of the objects, I thought of the objects, I thought of the objects, I thought of the objects, I thought of the objects, I thought of the objects, I thought of the objects, I thought of the objects, I thought of the objects, An element here is called theta. So theta is a G-morph in H3H3.

27:30 What does a G-morph mean in H3H3? Well, I want to associate something... Here, I want to associate something with U. So I have U, a glass of ice. And then I have U in H3H3. To be able to... I give myself this, and I look for, I don't do that, I have to go from the line with U to the U, so I have to go from the line with U to the U, and I have to go from the line with U to the U, and I have to go from the line with U to the U, and I have to go from the line with U to the U, and I have to go from the line with U to the U, and I have to go from the line with U to the U, and I have to go from the line with U to the U, and I have to go from the line with U to the U, So, to talk about the limit of relativity in these photos, I'm looking to go from G to U. So, I'm amortizing from G to R. So, I'm amortizing from G to V in F' . And U is sent in F . So, by reflection, it goes in F . So it's not over yet, we're doing this tutorial in U. I'm going to show you that if I have an arrow, I get a prime, I get an U, I get a prime, I get a prime. So what do I do? What do I do? I just build for each U, for each U. I gave myself a piece of this piece of paper I had in this toilet,

30:00 and I showed for each U that this was what I was doing. In short, we would like to introduce you to a series of lectures on mathematics, geometry, algebra, mathematics, and spin theory. Thank you for your attention. So, the question is in the other direction. So, the question is in the other direction. So, I am given... I am given... I am given... So, I am given... So, I am given... So, I am given... So, I am given... So, I am given... So, I am given... So, I am given... If you want to go from A to B, you have to go from A to B, then from A to B, and from A to B, and from A to B, and from A to B, and from A to B, and from A to B, and from A to B, and from A to B, and from A to B, and from A to B.

32:30 In this case, I will take Ft of v, in this case, I will take Ft of v, in this case, I will take Ft of v, in this case, I will take Ft of v, These are the two G's. And in particular, in this first one here, the G of G can be taken from the G of G to the G of G. So, if the G of C is the G of G, you can see it well because it is the same thing. If the G of G is the G of G, it can be taken from the G of G to the G of G. This is an object. I'm going to show you the two applications that are there on the other side of the screen. I'm going to show you the applications that compare the two. There is also a mini-projective that I made for you in B, in A0 of C, the sum of A, A, A, B, and B, the multiplication of A and B, and B, and B, and B, and B, and B, and B, and B, and B, and B, and B, and B, and B, and B, and B, and B, and B.

35:00 So we can try to write formulas, as I said in the first lecture, and write formulas. But in fact, if we do it seriously, it's a bit difficult too. So, well, finally, we will come back to the summary. I will explain to you what these categories belong to. You see, you have C and Y, so C is the denominator, and U is the derivative. So, this is the category that we named C, Y, U. But in fact, it's not this one, because you have to avoid the contravariants. And so, in fact, it's the opposite. These are the categories C, Y and O.

37:30 Contravariance is a new project which is called contravariance, but it works well because it is contravariant. So, it is a very good strategy. So, CERN, CERN Transition, and its operations are posterior. And if you have... The first piece of the script is B. I'm going to tell you that the first piece of the script is composed, it's very easy, and I say that B has to be confronted with some... all the conditions are the same, it's R, A, S, B, A, C, D, A, C, D. There, there's no problem. Then, the... So, in fact, in history, S, D, A, G, D, A, G, D, A, G, D, A, G, D, A, G, D, A, G, D, A, G, D, A, G, D, A, G, D, A, G, D, A, G, D, A, G, D, A, G, D, A, G, D, A, G, D, A, G, D, A, G, D, A, G, D, A, G, D, A, G, D, A, G, D, A, G, D, A, G, D, A, G, D, A, G, D, A, G, D, A, G, D, A, G, D, A, G, D, A, G, D, A, G, D, A, G, D, A, G, D, A, G, D, A, G So, in this case, you have a direct image. So, you have a set of terms and a theory. You want to take a direct image on Z. So, I can tell you that the water is open to Z. To find out the water, you have to do this on W. So, you have to say that the water is open to Z. That means that the water is open by analogy. So, the water is open to Z. Well, by the functions, for example, s equals s multiplied by dp divided by dv, which is the definition, we have s multiplied by st multiplied by dv and st multiplied by st multiplied by st multiplied by st multiplied by st multiplied by st multiplied by st multiplied by st multiplied by st multiplied by st multiplied by st multiplied by st multiplied by st multiplied by st multiplied by st multiplied by st

40:00 So, the second, so there is a, so we apply the formula once, we apply the formula, it's a technique, it's the case. For example, because that's the, as you can see, what we're going to do, we're going to compose two equations, and the equation is composed, because the equation is one, and the equation is one. All of this, for example, because, I repeat, if you have categories C, C' and C' and counters F and G' and G'. I write less and less, so I write less and less, so I write less and less, so I write less and less, so I write less and less, so I write less and less, so I write less and less, so I write less and less, so I write less and less, so I write less and less, so I write less and less.

42:30 Let's look at a particular case that corresponds to the description of a new object. So you have Y, which is a prefix, and then you take U, which is also a prefix. If you look at the category of the prefix U, you will see that it is a prefix. U is the category of objects that are part of a verbiage. Thank you for your attention. And we have a morphing called J-U of C-U, J-U-T, sorry. J-U-T of C-U of C-U. This morphing has a place of V in U. It's a V-D.

45:00 So if you want to use your intuition and think of the psychological space, you have here in the psychological space, there is a universe, and your theory of the country is the theory of the universe, and the country divided by the river, the river is the universe, and the river is the river, and the river is the river, and the river is the river, and the river is the river. There is a technical universe, which is a unique universe, like this one here, A, B, or U. When you say B, you will see that it is not the same thing. So there is a technical morphine of U and U. So there is a technical morphine. But on the other hand, there is no application that is unique. It is unique because it is unique. Thank you for watching this video. Thank you for watching this video.