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Semidirect Products and Split Short Five Lemma in Normal Categories

2013-11-28Artigo científico Acesso aberto
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datacite.subject.fosCiências Naturais::Matemáticas
datacite.subject.fosCiências Naturais::Ciências da Computação e da Informação
datacite.subject.sdg09:Indústria, Inovação e Infraestruturas
datacite.subject.sdg12:Produção e Consumo Sustentáveis
dc.contributor.authorMartins-Ferreira, Nelson
dc.contributor.authorMontoli, Andrea
dc.contributor.authorSobral, Manuela
dc.date.accessioned2026-07-07T14:12:18Z
dc.date.available2026-07-07T14:12:18Z
dc.date.issued2013-11-28
dc.description.abstractIn this paper we study a generalization of the notion of categorical semidirect product, as defined in [6], to a non-protomodular context of categories where internal actions are induced by points, like in any pointed variety. There we define semidirect products only for regular points, in the sense we explain below, provided the Split Short Five Lemma between such points holds, and we show that this is the case if the category is normal, as defined in [12]. Finally, we give an example of a category that is neither protomodular nor Mal’tsev where such generalized semidirect products exist.eng
dc.description.sponsorshipResearch partially supported by the Centre forMathematics of the University of Coimbra and Fundação para a Ciência e a Tecnologia, through European program COMPETE/FEDER and grants number PTDC/MAT/120222/2010, SFRH/BPD/43216/2008 and SFRH/BPD/69661/2010; also by ESTG and CDRSP from the Polytechnical Institute of Leiria.
dc.identifier.citationMartins-Ferreira, N., Montoli, A. & Sobral, M. Semidirect Products and Split Short Five Lemma in Normal Categories. Appl Categor Struct 22, 687–697 (2014). https://doi.org/10.1007/s10485-013-9344-5.
dc.identifier.doi10.1007/s10485-013-9344-5
dc.identifier.eissn1572-9095
dc.identifier.issn0927-2852
dc.identifier.urihttp://hdl.handle.net/10400.8/16555
dc.language.isoeng
dc.peerreviewedyes
dc.publisherSpringer Nature
dc.relationCategorical Methods in Non Abelian Algebra
dc.relationDESCENT OF INTERNAL CATEGORIES RELATIVE TO SPLIT EPIS
dc.relationNON ABELIAN HOMOLOGY AND COHOMOLOGY IN ACTION ACCESSIBLE CATEGORIES
dc.relation.hasversionhttps://link.springer.com/article/10.1007/s10485-013-9344-5
dc.relation.ispartofApplied Categorical Structures
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/
dc.subjectInternal actions
dc.subjectNormal categories
dc.subjectRegular points
dc.subjectSemidirect products
dc.titleSemidirect Products and Split Short Five Lemma in Normal Categorieseng
dc.typejournal article
dspace.entity.typePublication
oaire.awardNumberPTDC/MAT/120222/2010
oaire.awardNumberSFRH/BPD/43216/2008
oaire.awardNumberSFRH/BPD/69661/2010
oaire.awardTitleCategorical Methods in Non Abelian Algebra
oaire.awardTitleDESCENT OF INTERNAL CATEGORIES RELATIVE TO SPLIT EPIS
oaire.awardTitleNON ABELIAN HOMOLOGY AND COHOMOLOGY IN ACTION ACCESSIBLE CATEGORIES
oaire.awardURIhttp://hdl.handle.net/10400.8/13336
oaire.awardURIhttp://hdl.handle.net/10400.8/13633
oaire.awardURIhttp://hdl.handle.net/10400.8/16354
oaire.citation.endPage697
oaire.citation.issue5-6
oaire.citation.startPage687
oaire.citation.titleApplied Categorical Structures
oaire.citation.volume22
oaire.fundingStream5876-PPCDTI
oaire.fundingStreamFARH
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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In this paper we study a generalization of the notion of categorical semidirect product, as defined in [6], to a non-protomodular context of categories where internal actions are induced by points, like in any pointed variety. There we define semidirect products only for regular points, in the sense we explain below, provided the Split Short Five Lemma between such points holds, and we show that this is the case if the category is normal, as defined in [12]. Finally, we give an example of a category that is neither protomodular nor Mal’tsev where such generalized semidirect products exist.
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