cover-preserving functor

If $C$ and $D$ are sites, a functor $F\colon C\to D$ is **cover-preserving** (some people say **continuous**) if whenever $R$ is a covering family of an object $U\in C$, its image $F(R)$ is a covering family of $F(U)$ in $D$.

If $F$ is also flat, then it is called a morphism of sites, and induces a geometric morphism between sheaf toposes.

Created on November 7, 2010 at 18:15:50. See the history of this page for a list of all contributions to it.