Title
On principally generated quantaloid-modules in general, and skew local homeomorphisms in particularOn principally generated quantaloid-modules in general, and skew local homeomorphisms in particular
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Research group
Fundamental Mathematics
Publication type
article
Publication
Amsterdam,
Subject
Mathematics
Source (journal)
Annals of pure and applied logic. - Amsterdam
Volume/pages
161(2009):1, p. 43-65
ISSN
0168-0072
ISI
000271342400002
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
Ordered sheaves on a small quantaloid Q have been defined in terms of a-enriched categorical structures; they forma locally ordered category Ord (Q). The free-cocompletion KZ-doctrine on Ord(Q) has Mod(Q), the quantaloid of Q-modules, as its category of Eilenberg-Moore algebras. In this paper we give an intrinsic description of the Kleisli algebras: we call them the locally principally generated Q-modules. We deduce that Ord(Q) is biequivalent to the 2-category of locally principally generated Q-modules and left adjoint module morphisms. The example of locally principally generated modules on a locale X is worked out in full detail: relating X-modules to objects of the slice category LoC/(X), we show that ordered sheaves on X correspond with skew local homeomorphisms into X (like sheaves on X correspond with local homeomorphisms into X). (C) 2009 Elsevier B.V. All rights reserved.
Full text (open access)
https://repository.uantwerpen.be/docman/irua/0bcb4b/1197.pdf
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