nLab cover-preserving functor

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

If FF 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 18:15:51. See the history of this page for a list of all contributions to it.