1
vote
2answers
32 views

Precomposition with a faithful functor

If $F: C \rightarrow D$ is a faithful functor, then is the precomposition with $F$ functor $F^{\star}:[D:\mathbf{Set}] \rightarrow [C:\mathbf{Set}]$ faithful?
4
votes
1answer
91 views

How to get a geometric morphism out of a section? (And general pedagogy on classifying toposes)

Let $\mathcal{E}$ and $\mathcal{F}$ be toposes, $X$ an object of $\mathcal{E}$ and $p: \mathcal{E}/X \rightarrow \mathcal{E}$ the canonical geometric morphism (whose inverse image part is pullback ...
6
votes
1answer
219 views

An example of a Grothendieck topology

A Grothendieck topology on a category $\mathcal{C}$ with finite limits consists of, for each object $U$ in $\mathcal{C}$ a collection $\text{Cov}(U)$ of sets $\{ U_i \to U \}$ such that Isomorphisms ...