Thus we only need to prove that F is full. Thus F is a full embedding. An affine scheme over C is a geometric locale over C isomorphic to the spectrum of some object of C . Suppose C is a strict framed site with colimits. E are two bicontinuous functors.
Y are open effective.
D are then bicontinuous functors. Thus we can talk about base extension for framed sites. Note that any framed site is naturally an Loc -metric site. Consider the opposite Ring op of the category Ring of small commutative rings with 1 . Ring op is a locally small category with colimits, which is a strict effective framed site with the topology sending each commutative ring R to the frame of radical ideals of R .