Publication
Title
Modules on involutive quantales : canonical Hilbert structure, applications to sheaf theory
Author
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.
Language
English
Source (journal)
Order. - Dordrecht
Publication
Dordrecht : 2009
ISSN
0167-8094
Volume/pages
26:2(2009), p. 177-196
ISI
000267787100007
Full text (Publisher's DOI)
Full text (publisher's version - intranet only)
UAntwerpen
Faculty/Department
Research group
Publication type
Subject
Affiliation
Publications with a UAntwerp address
External links
Web of Science
Record
Identification
Creation 24.02.2012
Last edited 23.06.2017
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