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 18:15:50 by Mike Shulman (71.137.3.108)