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Cancellative conjugation semigroups and monoids

2019-11-21Journal 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.authorGarrão, A. P.
dc.contributor.authorMartins-Ferreira, Nelson
dc.contributor.authorRaposo, M.
dc.contributor.authorSobral, M.
dc.date.accessioned2025-09-11T15:41:53Z
dc.date.available2025-09-11T15:41:53Z
dc.date.issued2019-11-21
dc.description.abstractWe show that the category of cancellative conjugation semigroups is weakly Mal’tsev and give a characterization of all admissible diagrams there. In the category of cancellative conjugation monoids we describe, for Schreier split epimorphisms with codomain B and kernel X, all morphisms h: X→ B which induce a reflexive graph, an internal category or an internal groupoid. We describe Schreier split epimorphisms in terms of external actions and consider the notions of precrossed semimodule, crossed semimodule and crossed module in the context of cancellative conjugation monoids. In this category we prove that a relative version of the so-called “Smith is Huq” condition for Schreier split epimorphisms holds as well as other relative conditions.eng
dc.description.sponsorshipWe are grateful to the anonymous referees for their comments and suggestions that greatly contributed to the improvement of a previous version. This work was partially supported by Fundação para a Ciência e a Tecnologia (FCT) via: (CDRSP–UID/Multi/04044/2019) and (CMUC – UID/MAT/00324/2019); PAMI - ROTEIRO/0328/2013 (N022158); Next.parts (17963); Centro2020; CDRSP and ESTG from the Polytechnic Institute of Leiria, Centro de Matemática da Universidade de Coimbra, Faculdade de Ciências e Tecnologia da Universidade dos Açores.
dc.identifier.citationGarrão, A.P., Martins-Ferreira, N., Raposo, M. et al. Cancellative conjugation semigroups and monoids. Semigroup Forum 100, 806–836 (2020). https://doi.org/10.1007/s00233-019-10070-9.
dc.identifier.doi10.1007/s00233-019-10070-9
dc.identifier.eissn1432-2137
dc.identifier.issn0037-1912
dc.identifier.urihttp://hdl.handle.net/10400.8/14054
dc.language.isoeng
dc.peerreviewedyes
dc.publisherSpringer Nature
dc.relationCentre for Rapid and Sustainable Product Development
dc.relationCenter for Mathematics, University of Coimbra
dc.relation.hasversionhttps://link.springer.com/article/10.1007/s00233-019-10070-9
dc.relation.ispartofSemigroup Forum
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/
dc.subjectAdmissibility diagrams
dc.subjectWeakly Mal’tsev category
dc.subjectConjugation Semigroups
dc.subjectInternal monoid
dc.subjectInternal groupoid
dc.titleCancellative conjugation semigroups and monoidseng
dc.typejournal article
dspace.entity.typePublication
oaire.awardTitleCentre for Rapid and Sustainable Product Development
oaire.awardTitleCenter for Mathematics, University of Coimbra
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UID%2FMulti%2F04044%2F2019/PT
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UID%2FMAT%2F00324%2F2019/PT
oaire.citation.endPage836
oaire.citation.startPage806
oaire.citation.titleSemigroup Forum
oaire.citation.volume100
oaire.fundingStream6817 - DCRRNI ID
oaire.fundingStream6817 - DCRRNI ID
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
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.nameFundação para a Ciência e a Tecnologia
project.funder.nameFundação para a Ciência e a Tecnologia
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We show that the category of cancellative conjugation semigroups is weakly Mal’tsev and give a characterization of all admissible diagrams there. In the category of cancellative conjugation monoids we describe, for Schreier split epimorphisms with codomain B and kernel X, all morphisms h: X→ B which induce a reflexive graph, an internal category or an internal groupoid. We describe Schreier split epimorphisms in terms of external actions and consider the notions of precrossed semimodule, crossed semimodule and crossed module in the context of cancellative conjugation monoids. In this category we prove that a relative version of the so-called “Smith is Huq” condition for Schreier split epimorphisms holds as well as other relative conditions.
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