Enlarging B if necessary we may assume that B consists of all the affine objects. If X is any object of C , an effective open subset U of X is called affine if the open effective subobject U is affine. We first study separated morphisms in an algebraic site C . Denote by f ' the restriction of f to V . Suppose U is an open affine neighborhood of x contained in U '.
X U is affine.
Suppose f is separated. V is a closed special morphism. Y is a morphism. The other direction is obvious. Suppose X is an object.