Categorical structures enriched in a quantaloid: orders and ideals over a base quantaloid
| dc.creator | Stubbe, Isar | |
| dc.date | 2004-09-24 | |
| dc.date.accessioned | 2026-07-07T05:12:33Z | |
| dc.date.available | 2026-07-07T05:12:33Z | |
| dc.description | Applying (enriched) categorical structures we define the notion of ordered sheaf on a quantaloid Q, which we call `Q-order'. This requires a theory of semicategories enriched in the quantaloid Q, that admit a suitable Cauchy completion. There is a quantaloid Idl(Q) of Q-orders and ideal relations, and a locally ordered category Ord(Q) of Q-orders and monotone maps; actually, Ord(Q)=Map(Idl(Q)). In particular is Ord(Omega), with Omega a locale, the category of ordered objects in the topos of sheaves on Omega. In general Q-orders can equivalently be described as Cauchy complete categories enriched in the split-idempotent completion of Q. Applied to a locale Omega this generalizes and unifies previous treatments of (ordered) sheaves on Omega in terms of Omega-enriched structures. | |
| dc.description | 21 pages | |
| dc.identifier | https://arxiv.org/abs/math/0409477 | |
| dc.identifier | http://arxiv.org/abs/math/0409477 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72615 | |
| dc.subject | Category Theory | |
| dc.title | Categorical structures enriched in a quantaloid: orders and ideals over a base quantaloid | |
| dc.type | text |