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A Note on the “Smith is Huq” Condition

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.authorVan der Linden, Tim
dc.date.accessioned2026-01-15T15:03:29Z
dc.date.available2026-01-15T15:03:29Z
dc.date.issued2010-07-07
dc.description.abstractWe show that two known conditions which arose naturally in commutator theory and in the theory of internal crossed modules coincide: every starmultiplicative graph is multiplicative if and only if every two ef fective equivalence relations commute as soon as their normalisations do. This answers a question asked by George Janelidze.eng
dc.description.sponsorshipThanks to Tomas Everaert, Julia Goedecke and the referee for interesting suggestions and for their comments on the text.
dc.identifier.citationMartins-Ferreira, N., Van der Linden, T. A Note on the “Smith is Huq” Condition. Appl Categor Struct 20, 175–187 (2012). https://doi.org/10.1007/s10485-010-9231-2
dc.identifier.doi10.1007/s10485-010-9231-2
dc.identifier.issn0927-2852
dc.identifier.issn1572-9095
dc.identifier.urihttp://hdl.handle.net/10400.8/15348
dc.language.isoeng
dc.peerreviewedyes
dc.publisherSpringer
dc.relation.hasversionhttps://link.springer.com/article/10.1007/s10485-010-9231-2
dc.relation.ispartofApplied Categorical Structures
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subjectCommutator
dc.subjectInternal reflexive graph
dc.subjectStar-multiplication
dc.subjectGroupoid
dc.subjectProtomodular category
dc.subjectSemi-abelian category
dc.titleA Note on the “Smith is Huq” Conditioneng
dc.typejournal article
dspace.entity.typePublication
oaire.citation.endPage187
oaire.citation.issue2
oaire.citation.startPage175
oaire.citation.titleApplied Categorical Structures
oaire.citation.volume20
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
relation.isAuthorOfPublication52406f6a-2c36-4e9a-9996-d3cc719d46bf
relation.isAuthorOfPublication.latestForDiscovery52406f6a-2c36-4e9a-9996-d3cc719d46bf

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