Topological representation of sheaf cohomology of sites

For a site S (with enough points), we construct a topological space X(S) and a full embedding φ of the category of sheaves on S into those on X(S) (i.e., a morphism of toposes φ: Sh(X(S)) → Sh(S)). The embedding will be shown to induce a full embedding of derived categories, hence isomorphisms H(S, A) = H∗(X(S), φ A) for any abelian sheaf A on S. As a particular case, this will give for any scheme Y a topological space X(Y ) and a functorial isomorphism between the étale cohomology H(Yét, A) and the ordinary sheaf cohomology H ∗(X(Y ), φ A), for any sheaf A for the étale topology on Y .