There is a simple notion of what is a local homeomorphism of locales, along with the theorem: given a locale L then the full subcategory of Loc/L whose objects are local homeos is equivalent to Sheaves on L. All this can be found in Joyal-Tierney monograph "An extension of the Galois theory of Grothendieck". The definition of local homeo extends to toposes. But then the theorem becomes trivial: if E->F is a local homeo of toposes then there is an object I of F such that E is equivalent to F/I. If we want results for toposes that are more concrete and less trivial Peter Freyd's suggestion seems the way to go: replace sets by complete boolean algebras^op and use Barr's theorem that says that to any Grothendieck topos is covered (in the sense of having a surjective geometric morphism to it) by a topos of sheaves over a CBA. F Lamarche +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++