I am very new to topos theory and am interested in a couple little properties of a certain elementary topos.
Suppose $S$ is a small concrete category.
Then I was wondering.. which of there properties does the topos $[S:Sets]$ have:
- small (co)generating set *(particularly, what is it, would it be the initial object)?
- Has enough projective objects (particularly, is the initial object projective)?
So far, I know its locally small, so that's a good start...
I know this is a long question, but I don't know where to start..