Lifting retracted diagrams with respect to projectable functors
| dc.creator | Wehrung, Friedrich | |
| dc.date | 2004-09-16 | |
| dc.date.accessioned | 2026-07-07T05:12:10Z | |
| dc.date.available | 2026-07-07T05:12:10Z | |
| dc.description | We prove a general categorical theorem that enables us to state that under certain conditions, the range of a functor is large. As an application, we prove various results of which the following is a prototype: If every diagram, indexed by a lattice, of finite Boolean (v,0)-semilattices with (v,0)-embeddings, can be lifted with respect to the $\Conc$ functor on lattices, then so can every diagram, indexed by a lattice, of finite distributive (v,0)-semilattices with (v,0-embeddings. If the premise of this statement held, this would solve in turn the (still open) problem whether every distributive algebraic lattice is isomorphic to the congruence lattice of a lattice. We also outline potential applications of the method to other functors, such as the $R\mapsto V(R)$ functor on von Neumann regular rings. | |
| dc.identifier | https://arxiv.org/abs/math/0409270 | |
| dc.identifier | http://arxiv.org/abs/math/0409270 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72489 | |
| dc.subject | General Mathematics | |
| dc.subject | Category Theory | |
| dc.subject | 18A30, 18A25, 18A20, 18A35, 06A12, 06D05, 08B25, 18A40, 19A49 | |
| dc.title | Lifting retracted diagrams with respect to projectable functors | |
| dc.type | text |