Publication
Title
On principally generated quantaloid-modules in general, and skew local homeomorphisms in particular
Author
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.
Language
English
Source (journal)
Annals of pure and applied logic. - Amsterdam
Publication
Amsterdam : 2009
ISSN
0168-0072
Volume/pages
161:1(2009), p. 43-65
ISI
000271342400002
Full text (Publisher's DOI)
Full text (open access)
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 06.08.2017
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