Lifting retracted diagrams with respect to projectable functors

Details Lifting retracted diagrams with respect to projectable functors Lifting retracted diagrams with respect to projectable functors

2004-09-16

arxiv.org/abs/math/0409270v1

Mathematics

General Mathematics

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Lifting retracted diagrams with respect to projectable functors does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Lifting retracted diagrams with respect to projectable functors, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Lifting retracted diagrams with respect to projectable functors will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-200157