I think the title says it all. Quillen's Theorem A says that a functor $F\colon C\to D$ induces a homotopy equivalence of classifying spaces if each fiber category $F/d$ with $d$ an object of $D$ is contractible. Now Moerdijk showed that in some sense the classifying topos of a category is weakly equivalent to the classifying space of the category, so one would guess there is a topos theoretic interpretation/proof of the theorem.

Question:Is there a topos theoretic interpretation/proof of Quillen's Theorem A?

covariantmodel structure. This is something that can be checked on the homotopy fibers, which turn out to be precisely the nerves of the overcategories in question. – Akhil Mathew Jun 3 '12 at 20:49