Intrinsic Schreier split extensions

Detalhes bibliográficos
Autor(a) principal: Montoli, Andrea
Data de Publicação: 2020
Outros Autores: Rodelo, Diana, Van der Linden, Tim
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.1/14169
Resumo: In the context of regular unital categories we introduce an intrinsic version of the notion of a Schreier split epimorphism, originally considered for monoids. We show that such split epimorphisms satisfy the same homological properties as Schreier split epimorphisms of monoids do. This gives rise to new examples of S-protomodular categories, and allows us to better understand the homological behaviour of monoids from a categorical perspective.
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spelling Intrinsic Schreier split extensionsSemidirect productsMonoidsMaltsevLemmaFibration of pointsJointly extremal-epimorphic pairRegular categoryUnital categoryProtomodular categoryMonoidJónsson–Tarski varietyIn the context of regular unital categories we introduce an intrinsic version of the notion of a Schreier split epimorphism, originally considered for monoids. We show that such split epimorphisms satisfy the same homological properties as Schreier split epimorphisms of monoids do. This gives rise to new examples of S-protomodular categories, and allows us to better understand the homological behaviour of monoids from a categorical perspective.Programma per Giovani Ricercatori "Rita Levi-Montalcini" - Italian government through MIURCentre for Mathematics of the University of Coimbra [UID/MAT/00324/2019]Portuguese Government through FCT/MECEuropean Regional Development Fund through the Partnership Agreement PT2020SpringerSapientiaMontoli, AndreaRodelo, DianaVan der Linden, Tim2021-06-01T00:30:19Z2020-062020-06-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.1/14169eng0927-285210.1007/s10485-019-09588-4info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-07-24T10:26:25Zoai:sapientia.ualg.pt:10400.1/14169Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:05:13.176590Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Intrinsic Schreier split extensions
title Intrinsic Schreier split extensions
spellingShingle Intrinsic Schreier split extensions
Montoli, Andrea
Semidirect products
Monoids
Maltsev
Lemma
Fibration of points
Jointly extremal-epimorphic pair
Regular category
Unital category
Protomodular category
Monoid
Jónsson–Tarski variety
title_short Intrinsic Schreier split extensions
title_full Intrinsic Schreier split extensions
title_fullStr Intrinsic Schreier split extensions
title_full_unstemmed Intrinsic Schreier split extensions
title_sort Intrinsic Schreier split extensions
author Montoli, Andrea
author_facet Montoli, Andrea
Rodelo, Diana
Van der Linden, Tim
author_role author
author2 Rodelo, Diana
Van der Linden, Tim
author2_role author
author
dc.contributor.none.fl_str_mv Sapientia
dc.contributor.author.fl_str_mv Montoli, Andrea
Rodelo, Diana
Van der Linden, Tim
dc.subject.por.fl_str_mv Semidirect products
Monoids
Maltsev
Lemma
Fibration of points
Jointly extremal-epimorphic pair
Regular category
Unital category
Protomodular category
Monoid
Jónsson–Tarski variety
topic Semidirect products
Monoids
Maltsev
Lemma
Fibration of points
Jointly extremal-epimorphic pair
Regular category
Unital category
Protomodular category
Monoid
Jónsson–Tarski variety
description In the context of regular unital categories we introduce an intrinsic version of the notion of a Schreier split epimorphism, originally considered for monoids. We show that such split epimorphisms satisfy the same homological properties as Schreier split epimorphisms of monoids do. This gives rise to new examples of S-protomodular categories, and allows us to better understand the homological behaviour of monoids from a categorical perspective.
publishDate 2020
dc.date.none.fl_str_mv 2020-06
2020-06-01T00:00:00Z
2021-06-01T00:30:19Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10400.1/14169
url http://hdl.handle.net/10400.1/14169
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0927-2852
10.1007/s10485-019-09588-4
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
institution RCAAP
reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
repository.mail.fl_str_mv
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