A criterion for reflectiveness of normal extensions

Detalhes bibliográficos
Autor(a) principal: Montoli, Andrea
Data de Publicação: 2016
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/10400.1/9668
Resumo: We give a new sufficient condition for the normal extensions in an admissible Galois structure to be reflective. We then show that this condition is indeed fulfilled when X is the (protomodular) reflective subcategory of S-special objects of a Barr-exact S-protomodular category C, where S is the class of split epimorphic trivial extensions in C. Next to some concrete examples where the criterion may be applied, we also study the adjunction between a Barr-exact unital category and its abelian core, which we prove to be admissible.
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spelling A criterion for reflectiveness of normal extensionsWe give a new sufficient condition for the normal extensions in an admissible Galois structure to be reflective. We then show that this condition is indeed fulfilled when X is the (protomodular) reflective subcategory of S-special objects of a Barr-exact S-protomodular category C, where S is the class of split epimorphic trivial extensions in C. Next to some concrete examples where the criterion may be applied, we also study the adjunction between a Barr-exact unital category and its abelian core, which we prove to be admissible.SapientiaMontoli, AndreaRodelo, DianaVan der Linden, Tim2017-04-07T15:57:17Z20162016-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.1/9668eng1370-1444AUT: DRO01261;info: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:RCAAP2023-07-24T10:21:10Zoai:sapientia.ualg.pt:10400.1/9668Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:01:33.466921Repositório 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 A criterion for reflectiveness of normal extensions
title A criterion for reflectiveness of normal extensions
spellingShingle A criterion for reflectiveness of normal extensions
Montoli, Andrea
title_short A criterion for reflectiveness of normal extensions
title_full A criterion for reflectiveness of normal extensions
title_fullStr A criterion for reflectiveness of normal extensions
title_full_unstemmed A criterion for reflectiveness of normal extensions
title_sort A criterion for reflectiveness of normal 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
description We give a new sufficient condition for the normal extensions in an admissible Galois structure to be reflective. We then show that this condition is indeed fulfilled when X is the (protomodular) reflective subcategory of S-special objects of a Barr-exact S-protomodular category C, where S is the class of split epimorphic trivial extensions in C. Next to some concrete examples where the criterion may be applied, we also study the adjunction between a Barr-exact unital category and its abelian core, which we prove to be admissible.
publishDate 2016
dc.date.none.fl_str_mv 2016
2016-01-01T00:00:00Z
2017-04-07T15:57:17Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
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status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10400.1/9668
url http://hdl.handle.net/10400.1/9668
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 1370-1444
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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
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