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

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journal contribution
posted on 09.07.2015, 11:59 by M. Bilkova, Alexander A. Kurz, Daniela Petrisan, J. Velebil
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.

History

Citation

Logical Methods in Computer Science, 2013, 9 (4), 8

Author affiliation

/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Computer Science

Version

VoR (Version of Record)

Published in

Logical Methods in Computer Science

Publisher

International Federation of Computational Logic

issn

1860-5974

Copyright date

2013

Available date

09/07/2015

Publisher version

http://www.lmcs-online.org/ojs/viewarticle.php?id=1154

Language

en