A Godement theorem for locales

Abstract

The classical Godement Theorem for manifolds, characterizing kernel pairs for submersions (cf. e.g. [15], LG IV §5), has been used by Pradines[12] as a crucial property for having a good theory of differentiable groupoids; in fact, he developed an axiomatic theory of categories in which Godement's and some other exactness properties hold, under the name of ‘Godement diptych’.