From Wikipedia: A concrete category is a category that is equipped with a faithful functor to the category of sets. This functor makes it possible to think of the obj …

Let $A$ be a small category, and let $X:=Psh(A)$ denote the category of presheaves on $A$. It is a theorem that for any such category $X$, there exists a small set $M$ of monomorp …

Let $C,C',D\in \operatorname{Cat}$, and consider the following strict pushout square $$\begin{matrix} C&\overset{f}{\to} &D^{op}\\ \downarrow^\pi&\swarrow&\downarr …

Convention: Before I start, please note that it is not going to be sufficient to assume that the topology is subcanonical or that the site $C$ has finite limits, since the applica …