{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:25:53Z","timestamp":1753881953768,"version":"3.41.2"},"reference-count":0,"publisher":"World Scientific Pub Co Pte Ltd","funder":[{"DOI":"10.13039\/501100007474","name":"Centro de Matem\u00e1tica, Universidade de Coimbra","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100007474","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007474","name":"Centro de Matem\u00e1tica, Universidade de Coimbra","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100007474","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Algebra Appl."],"abstract":"<jats:p> The aim of this work is to further develop the calculus of (internal) relations for a regular [Formula: see text]-category [Formula: see text]. To capture the enriched features of a regular [Formula: see text]-category and obtain a good calculus, the relations we work with are precisely the ideals in [Formula: see text]. We then focus on an enriched version of the 1-dimensional algebraic [Formula: see text]-permutable (also called Mal\u2019tsev) property and its well-known equivalent characterizations expressed through properties on ordinary relations. We introduce the notion of [Formula: see text]-Mal\u2019tsev category and show that these may be characterized through enriched versions of the above-mentioned properties adapted to ideals. Any [Formula: see text]-enrichment of a 1-dimensional Mal\u2019tsev category is necessarily an [Formula: see text]-Mal\u2019tsev category. We also give some examples of categories which are not Mal\u2019tsev categories, but are [Formula: see text]-Mal\u2019tsev categories. <\/jats:p>","DOI":"10.1142\/s0219498826502336","type":"journal-article","created":{"date-parts":[[2025,4,14]],"date-time":"2025-04-14T04:13:21Z","timestamp":1744604001000},"source":"Crossref","is-referenced-by-count":0,"title":["Enriched aspects of calculus of relations and 2-permutability"],"prefix":"10.1142","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2653-8090","authenticated-orcid":false,"given":"Maria Manuel","family":"Clementino","sequence":"first","affiliation":[{"name":"CMUC, Department of Mathematics, University of Coimbra, 3000-143 Coimbra, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4816-3234","authenticated-orcid":false,"given":"Diana","family":"Rodelo","sequence":"additional","affiliation":[{"name":"CMUC, Department of Mathematics, University of Coimbra, 3000-143 Coimbra, Portugal"},{"name":"Department de Mathematics, University of the Algarve, 8005-139 Faro, Portugal"}]}],"member":"219","published-online":{"date-parts":[[2025,5,8]]},"container-title":["Journal of Algebra and Its Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219498826502336","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,8]],"date-time":"2025-05-08T14:01:32Z","timestamp":1746712892000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0219498826502336"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,5,8]]},"references-count":0,"alternative-id":["10.1142\/S0219498826502336"],"URL":"https:\/\/doi.org\/10.1142\/s0219498826502336","relation":{},"ISSN":["0219-4988","1793-6829"],"issn-type":[{"type":"print","value":"0219-4988"},{"type":"electronic","value":"1793-6829"}],"subject":[],"published":{"date-parts":[[2025,5,8]]},"article-number":"2650233"}}