Components, complements and reflection formulas
| dc.creator | Pisani, Claudio | |
| dc.date | 2007-01-16 | |
| dc.date.accessioned | 2026-07-07T07:41:19Z | |
| dc.date.available | 2026-07-07T07:41:19Z | |
| dc.description | Some basic features of the simultaneous inclusion of discrete fibrations and discrete opfibrations in categories over a base category X are considered. In particular, we illustrate the formulas (|P)x = ten(x/X,P) ; (P|)x = hom(X/x,P) which give the reflection |P and the coreflection P| of a category P over X in discrete fibrations. The explicit use of the "tensor functor" ten := \comp(- \times -) : Cat/X \times Cat/X \to Set given by the components of products, allows a vast generalization of the corresponding analysis in the two-valued context. For any df A, the functor ten(A,-) : Cat/X \to Set has a right adjoint \neg A valued in dof's (and vice versa); such a complement operator, which in the two-valued case reduces to the classical complementation between lower and upper parts of a poset, turns out to be an effective tool in the set-valued context as well. Various applications of the formulas and of the accompanying conceptual frame are presented. | |
| dc.description | 59 pages | |
| dc.identifier | https://arxiv.org/abs/math/0701457 | |
| dc.identifier | http://arxiv.org/abs/math/0701457 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/122062 | |
| dc.subject | Category Theory | |
| dc.subject | 18Axx | |
| dc.title | Components, complements and reflection formulas | |
| dc.type | text |