For simplicity we shall write F for Spec . 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 .