Finite preorders and topological descent II: étale descent

Abstract

It is known that every effective (global-) descent morphism of topological spaces is an effective etale-descent morphism. On the other hand, in the predecessor of this paper we gave examples of: a descent morphism that is not an effective etale-descent morphism; an effective etale-descent morphism that is not a descent morphism. Both of the examples in fact involved only finite topological spaces, i.e. just finite preorders, and now we characterize the effective etale-descent morphisms of preorders/finite topological spaces completely.