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Normality for monoid monomorphisms

2023-11Artigo científico Acesso aberto
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datacite.subject.fosCiências Naturais::Matemáticas
datacite.subject.sdg03:Saúde de Qualidade
datacite.subject.sdg09:Indústria, Inovação e Infraestruturas
datacite.subject.sdg11:Cidades e Comunidades Sustentáveis
dc.contributor.authorMartins-Ferreira, Nelson
dc.contributor.authorSobral, Manuela
dc.date.accessioned2026-10-15T14:53:13Z
dc.date.available2026-10-15T14:53:13Z
dc.date.issued2023-11
dc.description.abstractIn the category of monoids we characterize monomorphisms that are normal, in an appropriate sense, to internal reflexive relations, preorders or equivalence relations. The zero-classes of such internal relations are first described in terms of convenient syntactic relations associated to them and then through the adjunctions associated with the corresponding normalization functors. The largest categorical equivalences induced by these adjunctions provide equivalences between the categories of relations generated by their zero-classes and the ones of monomorphisms that we suggest to call normal with respect to the internal relations considered. This idea, although being transverse to the literature in the field, has not in our opinion been presented and explored in full generality. The existence of adjoints to the normalization functors permits developing a theory of normal monomorphisms, thus extending many results from groups and protomodular categories to monoids and unital categories.eng
dc.description.sponsorshipThis work is supported by Fundação para a Ciência e a Tecnologia FCT/MCTES (PIDDAC) through the following Projects: Associate Laboratory ARISE LA/P/0112/2020; UIDP/04044/2020; UIDB/04-044/2020; PAMI - ROTEIRO/0328/2013 (N◦ 022158); MATIS (CENTRO-01-0145-FEDER-000014 - 3362); Generative.Thermodynamic; by CDRSP and ESTG from the Polytechnic Institute of Leiria.
dc.identifier.citationNelson Martins-Ferreira, Manuela Sobral, Normality for monoid monomorphisms, Indagationes Mathematicae, Volume 34, Issue 6, 2023, Pages 1207-1222, ISSN 0019-3577, https://doi.org/10.1016/j.indag.2023.03.007.
dc.identifier.doi10.1016/j.indag.2023.03.007
dc.identifier.issn0019-3577
dc.identifier.urihttp://hdl.handle.net/10400.8/17076
dc.language.isoeng
dc.peerreviewedyes
dc.publisherElsevier
dc.relationAdvanced Production and Intelligent Systems
dc.relationCentre for Rapid and Sustainable Product Development
dc.relation.hasversionhttps://www.sciencedirect.com/science/article/pii/S0019357723000289?via%3Dihub
dc.relation.ispartofIndagationes Mathematicae
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subjectInternal binary relations
dc.subjectZero-classes
dc.subjectClots
dc.subjectPositive cones
dc.subjectNormal subobjects
dc.subjectSyntactic relations
dc.titleNormality for monoid monomorphismseng
dc.typejournal article
dspace.entity.typePublication
oaire.awardNumberLA/P/0112/2020
oaire.awardNumberUIDP/04044/2020
oaire.awardTitleAdvanced Production and Intelligent Systems
oaire.awardTitleCentre for Rapid and Sustainable Product Development
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/LA%2FP%2F0112%2F2020/PT
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDP%2F04044%2F2020/PT
oaire.citation.endPage1222
oaire.citation.issue6
oaire.citation.startPage1207
oaire.citation.titleIndagationes Mathematicae
oaire.citation.volume34
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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In the category of monoids we characterize monomorphisms that are normal, in an appropriate sense, to internal reflexive relations, preorders or equivalence relations. The zero-classes of such internal relations are first described in terms of convenient syntactic relations associated to them and then through the adjunctions associated with the corresponding normalization functors. The largest categorical equivalences induced by these adjunctions provide equivalences between the categories of relations generated by their zero-classes and the ones of monomorphisms that we suggest to call normal with respect to the internal relations considered. This idea, although being transverse to the literature in the field, has not in our opinion been presented and explored in full generality. The existence of adjoints to the normalization functors permits developing a theory of normal monomorphisms, thus extending many results from groups and protomodular categories to monoids and unital categories.
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