Relation lifting, with an application to the many-valued cover modality
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F13%3A00208595" target="_blank" >RIV/68407700:21230/13:00208595 - isvavai.cz</a>
Alternative codes found
RIV/67985807:_____/13:00424950
Result on the web
<a href="http://dx.doi.org/10.2168/LMCS-9(4:8)2013" target="_blank" >http://dx.doi.org/10.2168/LMCS-9(4:8)2013</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.2168/LMCS-9(4:8)2013" target="_blank" >10.2168/LMCS-9(4:8)2013</a>
Alternative languages
Result language
angličtina
Original language name
Relation lifting, with an application to the many-valued cover modality
Original language 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 "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.
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/GAP202%2F11%2F1632" target="_blank" >GAP202/11/1632: Algebraic Methods in Proof Theory</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Logical Methods in Computer Science
ISSN
1860-5974
e-ISSN
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Volume of the periodical
9
Issue of the periodical within the volume
4:8
Country of publishing house
DE - GERMANY
Number of pages
48
Pages from-to
1-48
UT code for WoS article
000329566000006
EID of the result in the Scopus database
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