Sheaves as modules
Abstract
We revisit sheaves on locales by placing them in the context of the theory of quantale modules. The local homeomorphisms are identified with the Hilbert -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.
Cite
@article{arxiv.0711.4401,
title = {Sheaves as modules},
author = {Pedro Resende and Elias Rodrigues},
journal= {arXiv preprint arXiv:0711.4401},
year = {2012}
}
Comments
23 pages. Version 2 contains changes in structure in order to make the main results more explicit. Former section 4 has been eliminated. Added some material on matrix representations ($B$-sets), plus a proof that Hilbert modules with bases are locales (Lemma 3.14)