Topos of triads, music / Co-power objects / evening conversations (chit-chat) (contd.)

0:00 I will explain why I don't have a pencil for this, because it is difficult for students to fix and our curative is going to be the whole, the entire relation, the thing that relates everything to one. So relate everything in B to something in A. So if I now make everything in A the same, then obviously I'm going to relate everything in B. That's going to be 1 in A that's all I've got now. So it'll just be 1. So I'll just relate everything. This is an expression of the relation of the first condition with the second relation of the second condition, so what we need to do is to work out what these two things are, and this one is expressible as a callback.

2:30 Yes, so I've got, this is a pullback, so yeah, there's a pullback of the name of the page, along with this name, this name which is the name of the quote I, where I is going to be the image of Colin, and so you take this pullback, This T is the big set, and this S is going to be a cinema fullback, I think, and this is going to be the name of one of the plays where maths is on here, and this will be the end of my lecture class, and I'll check on what position A should be.

5:00 Next question, the comment says you can express exponentials as finite sums of combination objects across permutation objects across.

7:30 I'm wondering if you just suppose you can realize your exponentiation another way. I mean, I'm thinking perhaps that you can not only in a topos have objects and potions, but also the Stirling object. So that you're fortunate enough that the Q of X would be expressed as a somewhat more primitive thing, all of which have the same cardinality sense to it. But the law is more of a... it's even more objective than mathematics. It's much better than mathematics. It's not even good. It just uses less of an obstruction to this sort of thing than there is to objectifying combinations. No, I wanted to add a point here. Another thing I was interested in was the model. Keep in mind that you can build power objects with an object-classic binary exponential. In this case, it's a sort of basic object of proportions. No, you know, those are just generic equations. It was number one, you were one. Yeah, there is. But if you have a generic quotient, it's... So even in some of that set, there's a map into it. If you have a generic quotient and you have a map into its codonate, if you have an R3 quotient, you can...

10:00 Well, I think this doesn't work in the set, but... Thank you. Yeah, that's right. Because if you have your generic quotient and you take a map from an arbitrary quotient into it and look at the pre-images of the whole form of your generic quotient and the pre-images, the theory is that, yeah, you're taking a callback. And I have the Z, which is the F of Z, or Y. I can look at the preeminent... So when I call back this arbitrary quotient, the paper above Z is going to just have the same commonality as the paper above Y. So that's a generic quotient. It would have to have five of the four possible commonalities.

12:30 So it's something like Z. If you just take the protein out for a representative of that, it's a contragrant of these representatives, it is 150 different species. So there's one that's got the proteins of sort of the figure types, and that's what you do with the special sets. The special sets have lots of different simplices, but among those, there are those that have the same shape as the map. The math to this unique object, which tells you what's the shape of a given component. I admit this is not a completely canonical 12, but I appreciate the purpose of this example, of this unique object. I really appreciate it. I'm not sure about the, I'm not sure about the, the, the, the, the, the, the, the, the, the, the, the, the, the, the, Thank you.