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
|
|
DOI
|
|
|
|
10.1016/J.APAL.2009.05.001
|
|
Volume/pages
|
|
|
|
161
:1
(2009)
, p. 43-65
|
|
ISI
|
|
|
|
000271342400002
|
|
Full text (Publisher's DOI)
|
|
|
|
|
|
Full text (open access)
|
|
|
|
|
|