On principally generated Q-modules in general, and skew local homeomorphisms in particular
| dc.creator | Heymans, Hans | |
| dc.creator | Stubbe, Isar | |
| dc.date | 2008-02-01 | |
| dc.date | 2009-05-05 | |
| dc.date.accessioned | 2026-07-07T13:11:06Z | |
| dc.date.available | 2026-07-07T13:11:06Z | |
| dc.description | Ordered sheaves on a small quantaloid Q have been defined in terms of Q-enriched categorical structures; they form a locally ordered category Ord(Q). The free-cocompletion KZ-doctrine on Ord(Q) has Mod(Q), the quantaloid of Q-modules, as 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). | |
| dc.description | 41 pages, revised version accepted for publication | |
| dc.identifier | https://arxiv.org/abs/0802.0097 | |
| dc.identifier | http://arxiv.org/abs/0802.0097 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/229182 | |
| dc.subject | Category Theory | |
| dc.title | On principally generated Q-modules in general, and skew local homeomorphisms in particular | |
| dc.type | text |