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We take a fresh look at the connection between lax extensions and predicate liftings from the point of view of quantale-enriched relations. Using this perspective, we show in particular that various fundamental concepts and results arise naturally and their proofs become very elementary. Ultimately, we prove that every lax extension is induced by a class of predicate liftings; we discuss several implications of this result.<\/jats:p>","DOI":"10.1017\/s096012952300035x","type":"journal-article","created":{"date-parts":[[2023,12,1]],"date-time":"2023-12-01T07:20:00Z","timestamp":1701415200000},"page":"98-127","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":3,"title":["A point-free perspective on lax extensions and predicate liftings"],"prefix":"10.1017","volume":"34","author":[{"given":"Sergey","family":"Goncharov","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1082-6135","authenticated-orcid":false,"given":"Dirk","family":"Hofmann","sequence":"additional","affiliation":[]},{"given":"Pedro","family":"Nora","sequence":"additional","affiliation":[]},{"given":"Lutz","family":"Schr\u00f6der","sequence":"additional","affiliation":[]},{"given":"Paul","family":"Wild","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2023,12,1]]},"reference":[{"key":"S096012952300035X_ref9","unstructured":"Forster, J. , Goncharov, S. , Hofmann, D. , Nora, P. , Schr\u00f6der, L. and Wild, P. 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