Sheaves as modules

Resende, Pedro; Rodrigues, Elias

http://hdl.handle.net/10400.13/4106

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Authors

Resende, Pedro

Rodrigues, Elias

Abstract(s)

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.