All Questions

From my general experience I think for myself of what follows as some kind of taboo question for some reason: in my imagination, everybody wants an answer to this but somehow thinks it shall not be ...

Suppose that we have two Grothendieck sites, their associated sheaves $\mathcal{E}=\rm{Sh}(\bf{C},J)$ and $\mathcal{F}=\rm{Sh}(\bf{D},K)$ and a geometric surjection $f:\mathcal{E}\to\mathcal{F}$. This ...

A site C with pullbacks is subcanonical (all representable presheaves are sheaves) if and only if its codomain fibration $Arr(C) \to C$ is a prestack (all hom-presheaves are sheaves). Is there a ...

Let $T_1$ and $T_2$ be two Grothendieck topologies on the same small category $C$, and let $T_3 = T_1 \cup T_2$ (by which I mean the smallest Grothendieck topology on $C$ containing $T_1$ and $T_2$). ...