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On lax protomodularity for Ord-enriched categories

dc.contributor.authorClementino, Maria Manuel
dc.contributor.authorMontoli, Andrea
dc.contributor.authorRodelo, Diana
dc.date.accessioned2023-03-28T12:10:01Z
dc.date.available2023-03-28T12:10:01Z
dc.date.issued2023
dc.description.abstractOur main focus concerns a possible lax version of the algebraic property of protomodularity for Ord -enriched categories. Having in mind the role of comma objects in the enriched context, we consider some of the characteristic properties of protomodularity with respect to comma objects instead of pullbacks. We show that the equivalence between protomodularity and certain properties on pullbacks also holds when replacing conveniently pullbacks by comma objects in any finitely complete category enriched in Ord, and propose to call lax protomodular such Ord -enriched categories. We conclude by studying this sort of lax protomodularity for the category OrdAb of preordered abelian groups, equipped with a suitable Ord -enrichment, and show that OrdAb fulfills the equivalent lax protomodular properties with respect to the weaker notion of precomma object; we call such categories lax preprotomodular. (c) 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http:// creativecommons .org /licenses /by -nc -nd /4 .0/).pt_PT
dc.description.versioninfo:eu-repo/semantics/publishedVersionpt_PT
dc.identifier.doi10.1016/j.jpaa.2023.107348pt_PT
dc.identifier.issn0022-4049
dc.identifier.urihttp://hdl.handle.net/10400.1/19333
dc.language.isoengpt_PT
dc.peerreviewedyespt_PT
dc.publisherElsevierpt_PT
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/pt_PT
dc.subjectPreordered abelian groupspt_PT
dc.subjectProtomodular categoriespt_PT
dc.subjectOf preorderspt_PT
dc.subjectCategories enriched in the categorypt_PT
dc.titleOn lax protomodularity for Ord-enriched categoriespt_PT
dc.typejournal article
dspace.entity.typePublication
oaire.citation.issue8pt_PT
oaire.citation.startPage107348pt_PT
oaire.citation.titleJournal of Pure and Applied Algebrapt_PT
oaire.citation.volume227pt_PT
person.familyNameRodelo
person.givenNameDiana
person.identifier.ciencia-id6C16-FCF9-64A0
person.identifier.orcid0000-0002-4816-3234
person.identifier.ridAFH-8267-2022
person.identifier.scopus-author-id8216708900
rcaap.rightsopenAccesspt_PT
rcaap.typearticlept_PT
relation.isAuthorOfPublication311bbe08-1f8a-4c84-87e7-23ddd55c89a3
relation.isAuthorOfPublication.latestForDiscovery311bbe08-1f8a-4c84-87e7-23ddd55c89a3

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