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

Kód výsledku v 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>

Nalezeny alternativní kódy

RIV/67985807:_____/13:00424950

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/GAP202%2F11%2F1632" target="_blank" >GAP202/11/1632: Algebraické metody v teorii důkazů</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2013

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Logical Methods in Computer Science

ISSN

1860-5974

e-ISSN

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Svazek periodika

9

Číslo periodika v rámci svazku

4:8

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

48

Strana od-do

1-48

Kód UT WoS článku

000329566000006

EID výsledku v databázi Scopus

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