We revisit sheaves on locales by placing them in the context of the
theory of quantale modules. The local homeomorphisms p : X → B are identified
with the Hilbert B-modules that are equipped with a natural notion of basis. The
homomorphisms of these modules are necessarily adjointable, and the resulting self dual category yields a description of the equivalence between local homeomorphisms
and sheaves whereby morphisms of sheaves arise as the “operator adjoints” of the
inverse images of the maps of local homeomorphisms.
