An affine site is a strict metric site B with finite limits in which any object is separated and quasi-compact.
C preserves finite limits.
An algebraic variety over an algebraically closed field k is a separated and quasi-compact prevariety over k . For the remainder of this section we assume C is an algebraic site with an affine basis B . Any object of C which is isomorphic to an object of B is called an affine object . 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.