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/10316/89455
https://doi.org/10.1007/s10485-019-09588-4
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 ExtensionsFibration of points; Jointly extremal-epimorphic pair; Regular category; Unital category; Protomodular category; Monoid; Jónsson–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.Springer Verlag2020info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10316/89455http://hdl.handle.net/10316/89455https://doi.org/10.1007/s10485-019-09588-4enghttps://link.springer.com/article/10.1007%2Fs10485-019-09588-4Montoli, AndreaRodelo, DianaVan der Linden, Timinfo: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:RCAAP2022-05-25T02:47:58Zoai:estudogeral.uc.pt:10316/89455Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T21:09:45.830112Repositório 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
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.author.fl_str_mv Montoli, Andrea
Rodelo, Diana
Van der Linden, Tim
dc.subject.por.fl_str_mv Fibration of points; Jointly extremal-epimorphic pair; Regular category; Unital category; Protomodular category; Monoid; Jónsson–Tarski variety
topic 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
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/10316/89455
http://hdl.handle.net/10316/89455
https://doi.org/10.1007/s10485-019-09588-4
url http://hdl.handle.net/10316/89455
https://doi.org/10.1007/s10485-019-09588-4
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv https://link.springer.com/article/10.1007%2Fs10485-019-09588-4
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Springer Verlag
publisher.none.fl_str_mv Springer Verlag
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
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instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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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
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