Title
Modules on involutive quantales : canonical Hilbert structure, applications to sheaf theory Modules on involutive quantales : canonical Hilbert structure, applications to sheaf theory
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Publication type
article
Publication
Dordrecht ,
Subject
Mathematics
Source (journal)
Order. - Dordrecht
Volume/pages
26(2009) :2 , p. 177-196
ISSN
0167-8094
ISI
000267787100007
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
We explain the precise relationship between two module-theoretic descriptions of sheaves on an involutive quantale, namely the description via so-called Hilbert structures on modules and that via so-called principally generated modules. For a principally generated module satisfying a suitable symmetry condition we observe the existence of a canonical Hilbert structure. We prove that, when working over a modular quantal frame, a module bears a Hilbert structure if and only if it is principally generated and symmetric, in which case its Hilbert structure is necessarily the canonical one. We indicate applications to sheaves on locales, on quantal frames and even on sites.
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https://repository.uantwerpen.be/docman/iruaauth/cb83c3/aa510313.pdf
Handle