Sheaves as modules

Details Sheaves as modules Sheaves as modules

2007-11-28

arxiv.org/abs/0711.4401v2

Appl. Categ. Structures 18 (2010) 199-217

Mathematics

Category Theory

23 pages. Version 2 contains changes in structure in order to make the main results more explicit. Former section 4 has been e

Scientific paper

10.1007/s10485-008-9131-x

We revisit sheaves on locales by placing them in the context of the theory of quantale modules. The local homeomorphisms $p:X\to B$ 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 maps of local homeomorphisms.

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