Sheaves as modules

Pedro Resende; Elias Rodrigues

doi:10.1007/s10485-008-9131-x

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arXiv · 0711.4401

Sheaves as modules

Pedro Resende·Elias Rodrigues

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Abstract

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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BibTeX RIS

Pedro Resende, Elias Rodrigues. 2008-01-28. Sheaves as modules. https://doi.org/10.1007/s10485-008-9131-x

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