2nd Tape of discussions, incl. FW Lawvere, A Peruzzi & M Wright

0:00 As you have two spaces, the next crosswise depends on the three products. What we demonstrate is the tensor products. If they come from opposite sides, they would be in themselves a sort of non-communicative, but given they have a mean, they will communicate down here if they're not here. This is an illusion, an aspect. We first transform this into an inclusion. Of course, no product, tensor product, is a representable case, but it does extend into another. So, you could have large group objects in this. But there are also these kind of pseudo-group objects, which are x cross y, as long to y. And by the way, this includes the diagonal, actually. I mean, v equals b itself. Anyway, the multiplication of the group, the so-called group, logic group, is something like that. It satisfies the sociability insofar as it makes sense out of that.

2:30 What does that mean in terms of elements? What does it mean if you take some sort of understanding of elements in a spectrum of a small algebra B, like the polynomials of one variable or even . So if you want to sort of understand what an element of this is, it's a pair of figures. You get another figure of the same basic shape. For example, points. A pair of points would multiply to become a point. So it's only for some of the pairs. Some pairs go, of course, back and through, as though you had less than a group because you had a multiplication only in order. In a certain sense, you could say they commute. In the chronicles, it did make sense to think, you know, this is a special. It's commuting like property of figures. In that sense, only muting things. But in essence, those things that are developed can't even be compared.

5:00 Now this, I've never seen this explained ever. It was a hundred years now, and I've seen all this stuff on topology. See, the topology is different, but there is this tensor product of the grid categories. Also, there are two products, if you want to learn about that. So, in principle, whenever you look at the grid categories, they are just invective places. They have a geometry that comes through the product. See, this is really such an improper measurement of the...