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

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	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 %22powerset monad%22 on categories, one is the preservation by T of %22exactness%22 of certain squares. Both characterisations are generalisations of the %22classical%22 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. 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 %22powerset monad%22 on categories, one is the preservation by T of %22exactness%22 of certain squares. Both characterisations are generalisations of the %22classical%22 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. (en)
Title	Relation lifting, with an application to the many-valued cover modality Relation lifting, with an application to the many-valued cover modality (en)
skos:prefLabel	Relation lifting, with an application to the many-valued cover modality Relation lifting, with an application to the many-valued cover modality (en)
skos:notation	RIV/68407700:21230/13:00208595!RIV14-GA0-21230___
http://linked.open...avai/predkladatel	Fakulta elektrotechnická
http://linked.open...avai/riv/aktivita	I P
http://linked.open...avai/riv/aktivity	I, P(GAP202/11/1632)
http://linked.open...iv/cisloPeriodika	4:8
http://linked.open...vai/riv/dodaniDat	2014
http://linked.open...aciTvurceVysledku	Velebil, Jiří
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	České vysoké učení technické v Praze / Fakulta elektrotechnická
http://linked.open...dnocenehoVysledku	102161
http://linked.open...ai/riv/idVysledku	RIV/68407700:21230/13:00208595
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Relation lifting (en)
http://linked.open.../riv/klicoveSlovo	Relation lifting
http://linked.open...odStatuVydavatele	DE - Spolková republika Německo
http://linked.open...ontrolniKodProRIV	[F7895BFAA3F6]
http://linked.open...i/riv/nazevZdroje	Logical Methods in Computer Science
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	4 (xsd:int)
http://linked.open...vavai/riv/projekt	Algebraic Methods in Proof Theory
http://linked.open...UplatneniVysledku	2013
http://linked.open...v/svazekPeriodika	9
http://linked.open...iv/tvurceVysledku	Velebil, Jiří Kurz, A. Bílková, M. Petrisan, D.
http://linked.open...ain/vavai/riv/wos	000329566000006
issn	1860-5974
number of pages	48 (xsd:int)
http://bibframe.org/vocab/doi	10.2168/LMCS-9(4:8)2013
http://localhost/t...ganizacniJednotka	21230

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