Charles Ehresmann & category theory (contd.)

0:00 I would like to thank you all for being here today. Thank you very much. Thank you very much. Thank you. Thank you. Thank you. Thank you. Thank you. Thank you. Thank you. Thank you. Thank you. Thank you. In the previous lectures, we have discussed the importance of quantum mechanics. Witten has always spoken about quantum mechanics. It is clear that all the others have done so many great things. All of these questions were considered, but they were not of the same nature as the ones we discussed. We had a lot of choices. Yes, it is a question of science. As we said in the first session of the seminar, we warned about the science of mathematics, but at one point we decided to use it well to make the theory of species. The point of Weidman on the question is to look at the factors of reference, but only on the derivatives. So it goes on the side of Jean Choyal, who instituted this to reduce things, to calculate new interesting things, to count structures. But indeed, this is a case where if we had been able to look at something other than the derivatives ... We would have talked about thermodynamics in general.

2:30 Too far, Jean, please. I would like to ask you about what you said earlier about chromatic theory. At the same time, the theory of thermodynamics is never written, but there is a pearl at the end, namely the theory of the existence of C. It is precisely this client, except that there were no cathedrals at the time, and the hypotheses, the solutions, etc. It is by the way quite true that this is the first question. There are also many other fields of study, such as quantum mechanics, quantum mechanics, quantum mechanics, quantum mechanics, quantum mechanics, quantum mechanics, quantum mechanics, quantum mechanics, quantum mechanics, quantum mechanics, quantum mechanics, quantum mechanics, quantum mechanics, quantum mechanics, quantum mechanics, quantum mechanics, quantum mechanics, quantum mechanics, quantum mechanics, quantum mechanics, There is also a text by Saint-Germain that I found by chance in the French library. I found this text in the blog of Michael. I'm going to the photocopy. There are people who want to help me with the photocopies. You may have noticed that my head was there because it was a text of other people, of just a few people, of 4,000 people, of 5,000 people, of 5,000 people, of 5,000 people, of 5,000 people, of 5,000 people, of 5,000 people, of 5,000 people, of 5,000 people, of 5,000 people, of 5,000 people, of 5,000 people, of 5,000 people, of 5,000 people, of 5,000 people, of 5,000 people, of 5,000 people, of 5,000 people, of 5,000 people, of 5,000 people, of 5,000 people, of 5,000 people.

5:00 These terms are incompatible with what Cartier says, which is why our country is incompatible. Cartier basically says that we're going to keep the results in the next 200 years. That's why we're asking for a relationship between the public and the private sector. But in the end, Cromer says something else. Cromer says that no, no, the public sector is incompatible. Thank you for your attention. These are very convincing explanations, because we have had enough of them at the beginning of the debate. Can't we find the answer to the question, the answer to the question? Yes, the answer to the question is precisely in the introduction of a fundamental law, that is to say, what made the separations complete was the way of conceiving, either by the construction of the ensembles, by a concept of physics, which is typically the way of conceiving. And it's, in terms of thinking, it's... in law, it's not incompatible with... but in fact, yes, with all the conceptions, perhaps, yes, but the conceptions are different. MacLean, by the way, is right to say that he is in conflict with Bonaparte in his historical work on the image of the empire. No, Bonaparte is just missing. And indeed, I can't judge the total pertinence of your lecture, but it's also the universal construction of your lecture. That's the point of view of your lecture. The conception is at the end of the chapter 4 of the Mathematical Lecture, which is called... You were talking about the replicants of the last lecture.

7:30 There is a conference in which the director of physics talks about mathematics, or mathematics in general, and all that. They are all great partners. But this newspaper, man, it's not there. That's it. The next sentence, guys, is that no one in the Ministry of Health has ever spoken about this topic. And compared to what you said, it's true that he just made it up. The quotient by a filter. He never examined a product by a filter. He never looked at the capacity of a filter. So he included the notion of ultraproducts, their ecological utilisation, etc., etc., in order to generalise, to look at what is also local, what is practical, and what is not. At the end of each case, there is the category of the 70-year-old human being, in which it is understood that the importance is not the largest generation, but the generation of the next generation, the generation of the next generation, the generation of the next generation, the generation of the next generation, the generation of the next generation, the generation of the next generation, the generation of the next generation Thank you for your attention.

10:00 The topos of the terrestrial quality, that is to say the topos of the vessel, on the pre-hippocampus, are the topos of the human body. Yes, to have a topological topology, we really need very specific conditions on the categories, but at least inductive on the local category, to be asked completely regularly, because there are still very rare cases in Europe. And on the topology part, I'm going to share with you some of the students who have studied mathematics and the nature of their studies. I'm going to explain to them the relationship between mathematical physics and quantum mechanics. I'm going to explain to them the relationship between mathematical physics and quantum mechanics. The last thing I want to say is that mathematics is a tradition. The last two years. So, he, of course, does this kind of things. By the way, he's been doing it for a long time. But, unfortunately, it's because Braun is in the middle of the festival. Especially because he gives combinations. So, there is a combination with a categorical spirit of ancient physics. Which is practical, I must say. Maybe there is something else. But, again, a great deal of ancient physics. But now, this is not bad. I'm going to start with the last one, otherwise we're going to say that there were only 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 62, 62, 63, 62, 63, 62, 62, 63, 62, 62, 63, 62, 62, 63, 62, 62, 63, 62, 62, 63, 62, 62, 63, 62, 62, 63, 62, 63, 62, 63, 62, 63, 62, 63, 62, 63, 62, 63, 62

12:30 I would like to share with you an anecdote that is quite typical for me. When I started working with him, it was in a different geometry. He rejected a young man who loved mathematics and gave me the opportunity to write a book about the universe. And I said to him, We are totally incapable of doing that. But no, but no, ladies and gentlemen, we are quite capable of it. Anyway, everything in this book is in the two notes in the score. In the two notes in the score that you studied, that you understood. And it was true. That means that in the period, maybe I can explain that to you, The type of differential geometry he wrote very little, very little, and when he started to study the categories in particular, the categories on the side, the triplocos, etc., etc., that's when he learned how to do it, but otherwise, the first works, and yet it was the first works that were done quite a few times when I played differential geometry, 17 anecdotes, because I... I was in a daze when he told me that I was going to do a three-digit sum, and he told me that everything was in the two notes, and that it was all the same. Yes, all the important results of differential geometry are essentially in a series of notes that he puts between 52 and 56, 57.

15:00 To conclude with Michel's question about physics, after Pétain-Proulx, there are several others. Until 1970, Michel was a student of Hilbert. Hilbert was a student of Hilbert. Hilbert was a student of Hilbert. Hilbert was a student of Hilbert. So, there was Foss, who was in 1968, or something like that. Well, in a way, it's the same thing. Yes, I really think there are three periods in which the students... We can do another explanation to remember the history of this last school. There are some books that have not been... There is a very interesting one. The Chinese have written... Ah yes. The Chinese have written... The Chinese have written... The Chinese have written... That's why I forgot to mention that there was a co-director in Hermit for the seminars. There was a seminar for mathematics, a seminar for mathematics, and a seminar for mathematics. And, of course, the development of these kinds of knowledge was made possible by you. No, I'm sure there were a lot of notions that Charles was aware of by the fact that people were interested in fiber products, things like that. I would have probably, I would have probably, I've never seen that before, it's true, it's true, it's true.

17:30 You can hear me as you can hear me. I have spent a lot of time. I could not, how to say, if I took students, if I did a seminar, to do it in the language of A. S. Mann. Thank you very much.