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An observation on n-permutability

2014-05Journal article Open access
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datacite.subject.fosCiências Naturais::Matemáticas
datacite.subject.sdg03:Saúde de Qualidade
datacite.subject.sdg09:Indústria, Inovação e Infraestruturas
datacite.subject.sdg12:Produção e Consumo Sustentáveis
dc.contributor.authorMartins-Ferreira, Nelson
dc.contributor.authorRodelo, Diana
dc.contributor.authorVan der Linden, Tim
dc.date.accessioned2025-06-27T14:32:52Z
dc.date.available2025-06-27T14:32:52Z
dc.date.issued2014-05
dc.description.abstractWe prove that in a regular category all reflexive and transitive relations are symmetric if and only if every internal category is an internal groupoid. In particular, these conditions hold when the category is n-permutable for some n.eng
dc.description.sponsorshipThe first author was supported by IPLeiria/ESTG-CDRSP and Fundação para a Ciência e a Tecnologia (under grant number SFRH/BPD/4321/2008). The second author’s research was supported by CMUC, funded by the European Regional Development Fund through the program COMPETE and by the Portuguese Government through the FCT-Fundação para a Ciência e a Tecnologia under the project PEst-C/MAT/UI0324/2011. The third author is a Research Associate of the Fonds de la Recherche Scientifique–FNRS and would like to thank CMUC for its kind hospitality during his stay in Coimbra. All three were supported by the FCT Grant PTDC/MAT/120222/2010 through the European program COMPETE/FEDER.
dc.description.sponsorshipWe are grateful to the referee for his helpful comments and suggestions.
dc.identifier.citationNelson Martins-Ferreira, Diana Rodelo, Tim Van der Linden "An observation on n-permutability," Bulletin of the Belgian Mathematical Society - Simon Stevin, Bull. Belg. Math. Soc. Simon Stevin 21(2), 223-230, (may 2014). DOI: https://doi.org/10.36045/bbms/1400592620.
dc.identifier.doi10.36045/bbms/1400592620
dc.identifier.issn1370-1444
dc.identifier.urihttp://hdl.handle.net/10400.8/13444
dc.language.isoeng
dc.peerreviewedyes
dc.publisherBelgian Mathematical Society
dc.relationCategorical Methods in Non Abelian Algebra
dc.relation.hasversionhttps://projecteuclid.org/journals/bulletin-of-the-belgian-mathematical-society-simon-stevin/volume-21/issue-2/An-observation-on-n-permutability/10.36045/bbms/1400592620.full
dc.relation.ispartofBulletin of the Belgian Mathematical Society - Simon Stevin
dc.rights.uriN/A
dc.subjectMal’tsev category
dc.subjectGoursat category
dc.subjectn-permutable category
dc.subjectpre-order
dc.subjectequivalence relation
dc.subjectinternal category
dc.subjectinternal groupoid
dc.titleAn observation on n-permutabilityeng
dc.typejournal article
dspace.entity.typePublication
oaire.awardTitleCategorical Methods in Non Abelian Algebra
oaire.awardURIhttp://hdl.handle.net/10400.8/13336
oaire.citation.endPage230
oaire.citation.issue2
oaire.citation.startPage223
oaire.citation.titleBulletin of the Belgian Mathematical Society - Simon Stevin
oaire.citation.volume21
oaire.fundingStream5876-PPCDTI
oaire.versionhttp://purl.org/coar/version/c_970fb48d4fbd8a85
person.familyNameMartins-Ferreira
person.givenNameNelson
person.identifier485301
person.identifier.ciencia-idB115-B65E-24AA
person.identifier.orcid0000-0002-4199-7367
person.identifier.ridN-1699-2013
person.identifier.scopus-author-id24598020700
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We prove that in a regular category all reflexive and transitive relations are symmetric if and only if every internal category is an internal groupoid. In particular, these conditions hold when the category is n-permutable for some n.
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