{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,2]],"date-time":"2025-11-02T20:17:01Z","timestamp":1762114621501,"version":"build-2065373602"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2017,9,27]],"date-time":"2017-09-27T00:00:00Z","timestamp":1506470400000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"},{"start":{"date-parts":[[2017,9,27]],"date-time":"2017-09-27T00:00:00Z","timestamp":1506470400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"},{"start":{"date-parts":[[2017,9,27]],"date-time":"2017-09-27T00:00:00Z","timestamp":1506470400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,3,31]]},"abstract":"<jats:p>We show that, for a quantale $V$ and a $\\mathsf{Set}$-monad $\\mathbb{T}$ laxly extended to $V$-$\\mathsf{Rel}$, the presheaf monad on the category of $(\\mathbb{T},V)$-categories is simple, giving rise to a lax orthogonal factorisation system (lofs) whose corresponding weak factorisation system has embeddings as left part. In addition, we present presheaf submonads and study the LOFSs they define. This provides a method of constructing weak factorisation systems on some well-known examples of topological categories over $\\mathsf{Set}$.<\/jats:p><jats:p>Comment: 13 pages. Minor changes from previous version<\/jats:p>","DOI":"10.23638\/lmcs-13(3:32)2017","type":"journal-article","created":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:29:45Z","timestamp":1743701385000},"source":"Crossref","is-referenced-by-count":2,"title":["Lax orthogonal factorisations in monad-quantale-enriched categories"],"prefix":"10.23638","volume":"Volume 13, Issue 3","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2653-8090","authenticated-orcid":false,"given":"Maria Manuel","family":"Clementino","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9593-0571","authenticated-orcid":false,"given":"Ignacio Lopez","family":"Franco","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2017,9,27]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/1701.05510v5","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/1701.05510v5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:29:45Z","timestamp":1743701385000},"score":1,"resource":{"primary":{"URL":"http:\/\/lmcs.episciences.org\/2667"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,9,27]]},"references-count":0,"URL":"https:\/\/doi.org\/10.23638\/lmcs-13(3:32)2017","relation":{"has-preprint":[{"id-type":"arxiv","id":"1701.05510v4","asserted-by":"subject"},{"id-type":"arxiv","id":"1701.05510v3","asserted-by":"subject"},{"id-type":"arxiv","id":"1701.05510v2","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"1701.05510","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1701.05510","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2017,9,27]]},"article-number":"2667"}}