Re: Direct image functors

Dear Steve,

By the way, I looked at the Elephant to see what you said there, and I saw "we shall see later that, in a sense, f_* 'embodies the geometric aspects' of the morphism f". What did you have in mind for the "we shall see later"?

I'm not now sure exactly what I meant, but I believe I was thinking primarily of the fact that f_*: Sh(X) --> Sh(Y) points in the same direction as a continuous map f: X --> Y of spaces. On the other hand, my assertion that f^* `embodies the algebraic aspects' of f is certainly explained by A4.1 18 -- the fact that inverse image functors are unital morphisms of geometric allegories. Peter [For admin and other information see: http://www.mta.ca/~cat-dist/ ]