Categorical structures & cohomology (lecture 3) (contd.)

0:00 So, P admits the propriety of rising, not simply because they are in P1, but because, not even because I am in P2 or P3, but because... There is a great freedom without knowing how to write all the impossible extensions, but each time that from B1, B2 and B3 we can create a larger extension by the different properties that intervene in the terminations of the saturated families, there will be the possibility of revisions in relation to that. To be precise, we have to say a word for the proof of the corollary, it is done by the lemma. We had a lemma just before, before the theorem. The family of all these terms has the property of taking the definition of the definition and contains P1, and therefore contains the saturation of P1, which is none other than the definition of the extension.

2:30 So, in fact, the two and P3 here are used in illustration to know These are anonymous extensions that play a role in the saturation of B1. Everything that is in the saturation of B1 is lost, and in particular B2 and B3. The theorem tells us that B2 and B3 are in this saturation. So that's the demonstration. So, we still have to show the theorem. I'm going to sketch out the theorem's demonstration with the theorem. We can only make a sketch, it's important. I'm going to give you references. What I followed here is the book of Corse and Jardin, but what I noted in the proposition is that there is a number of chapters, perhaps in chapter 1, chapter 3 as well, which I cited last week, chapter 4, chapter 4. What's next? Well, we can say the following things, it's quite easy.