André JOYAL - 2/4 A crash course in topos theory : the big picture

I will sketch an overall picture of topos theory and of the theory of locales. It includes the notion of sheaf on a site, the notion of forcing topology, of geometric morphism and Giraud's theorem.
A useful principle is that a topos is a commutative ring-like object.
Every topos is a quotient of a free topos, like every commutative ring is a quotient of a polynomial ring.

Видео André JOYAL - 2/4 A crash course in topos theory : the big picture канала Institut des Hautes Études Scientifiques (IHÉS)