{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,4]],"date-time":"2023-09-04T08:18:24Z","timestamp":1693815504983},"reference-count":1,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2013,10,25]],"date-time":"2013-10-25T00:00:00Z","timestamp":1382659200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"We introduce basic notions and results about relation liftings on categories\nenriched in a commutative quantale. We derive two necessary and sufficient\nconditions for a 2-functor T to admit a functorial relation lifting: one is the\nexistence of a distributive law of T over the \"powerset monad\" on categories,\none is the preservation by T of \"exactness\" of certain squares. Both\ncharacterisations are generalisations of the \"classical\" results known for set\nfunctors: the first characterisation generalises the existence of a\ndistributive law over the genuine powerset monad, the second generalises\npreservation of weak pullbacks. The results presented in this paper enable us\nto compute predicate liftings of endofunctors of, for example, generalised\n(ultra)metric spaces. We illustrate this by studying the coalgebraic cover\nmodality in this setting.<\/jats:p>","DOI":"10.2168\/lmcs-9(4:8)2013","type":"journal-article","created":{"date-parts":[[2014,7,15]],"date-time":"2014-07-15T09:37:51Z","timestamp":1405417071000},"source":"Crossref","is-referenced-by-count":7,"title":["Relation lifting, with an application to the many-valued cover modality"],"prefix":"10.46298","volume":"Volume 9, Issue 4","author":[{"given":"Marta","family":"Bilkova","sequence":"first","affiliation":[]},{"ORCID":"http:\/\/orcid.org\/0000-0002-8685-5207","authenticated-orcid":false,"given":"Alexander","family":"Kurz","sequence":"additional","affiliation":[]},{"given":"Daniela","family":"Petrisan","sequence":"additional","affiliation":[]},{"given":"Jiri","family":"Velebil","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2013,10,25]]},"reference":[{"key":"738:not-found"}],"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/742\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/742\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,11]],"date-time":"2023-04-11T19:54:57Z","timestamp":1681242897000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/742"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,10,25]]},"references-count":1,"URL":"https:\/\/doi.org\/10.2168\/lmcs-9(4:8)2013","relation":{"is-same-as":[{"id-type":"arxiv","id":"1307.4682","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1307.4682","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"value":"1860-5974","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,10,25]]}}}