Relation lifting, with an application to the many-valued cover modality

0424950 - ÚI 2014 RIV DE eng J - Journal Article
Bílková, Marta - Kurz, A. - Petrisan, D. - Velebil, J.
Relation lifting, with an application to the many-valued cover modality.
Logical Methods in Computer Science. Roč. 9, č. 4 (2013), 8_1-8_48. ISSN 1860-5974. E-ISSN 1860-5974
R&D Projects: GA ČR GAP202/11/1632
Institutional support: RVO:67985807
Keywords : relation lifting * module * exact square * enriched categories * commutative quantale * coalgebra * modal logic * cover modality
Subject RIV: BA - General Mathematics
Impact factor: 0.443, year: 2013
http://www.lmcs-online.org/ojs/viewarticle.php?id=1154&layout=abstract

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.
Permanent Link: http://hdl.handle.net/11104/0230931