Bilkova, Marta and Kurz, Alexander and Petrisan, Daniela and Velebil, Jiri - Relation lifting, with an application to the many-valued cover modality

lmcs:742 - Logical Methods in Computer Science, October 25, 2013, Volume 9, Issue 4
Relation lifting, with an application to the many-valued cover modality

Authors: Bilkova, Marta and Kurz, Alexander and Petrisan, Daniela and Velebil, Jiri

We introduce basic notions and results about relation liftings on categories enriched in a commutative quantale. We derive two necessary and sufficient conditions for a 2-functor T to admit a functorial relation lifting: one is the existence of a distributive law of T over the "powerset monad" on categories, one is the preservation by T of "exactness" of certain squares. Both characterisations are generalisations of the "classical" results known for set functors: the first characterisation generalises the existence of a distributive law over the genuine powerset monad, the second generalises preservation of weak pullbacks. The results presented in this paper enable us to compute predicate liftings of endofunctors of, for example, generalised (ultra)metric spaces. We illustrate this by studying the coalgebraic cover modality in this setting.


Source : oai:arXiv.org:1307.4682
DOI : 10.2168/LMCS-9(4:8)2013
Volume: Volume 9, Issue 4
Published on: October 25, 2013
Submitted on: March 7, 2012
Keywords: Computer Science - Logic in Computer Science


Share

Consultation statistics

This page has been seen 58 times.
This article's PDF has been downloaded 31 times.