2nd talk/ Peter T Johnstone: 3rd talk (contd.)

0:00 So, viewing why, and not precisely the math, here's a locale, so she's on x, so this topos, inside she's on x, you see a compact locale, so it's a topo that's saying, intuitively speaking, it's saying that the fibers are compact, of course it's a little more complex, because the internal logic of the topos is not as polarized, apart from the fact that there are no, there may be some kind of problems. If you take the pullback on a proper map, along a proper subjection, and you obtain something that is proper, that is what you started with, what was already proper, and sometimes it is reflected by pullback down, published rejections, and then two and a half axioms, which have the easy pullback, which is out there in our name. If you take an equipments relation whose two legs are proper, then the coefficient of the co-equalizer is stable on the pullback, so we could try to replace.

2:30 One other thing which you may recognize from topology, namely, if you think of a triangle. Let's say, if this, and you might be interested in some other space, doesn't have complex parts. What that says is that these parts don't have to be called complex parts. There's a point of why it's not close to speaking of the four of them. But this is true in locale, but not in a household age problem.