Relation Liftings on Preorders and Posets
Logic in Computer Science
2012-10-05 v1 Category Theory
Abstract
The category Rel(Set) of sets and relations can be described as a category of spans and as the Kleisli category for the powerset monad. A set-functor can be lifted to a functor on Rel(Set) iff it preserves weak pullbacks. We show that these results extend to the enriched setting, if we replace sets by posets or preorders. Preservation of weak pullbacks becomes preservation of exact lax squares. As an application we present Moss's coalgebraic over posets.
Cite
@article{arxiv.1210.1433,
title = {Relation Liftings on Preorders and Posets},
author = {Marta Bilkova and Alexander Kurz and Daniela Petrisan and Jiri Velebil},
journal= {arXiv preprint arXiv:1210.1433},
year = {2012}
}