Semidirect Products and Split Short Five Lemma in Normal Categories
Autor(a) principal: | |
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Data de Publicação: | 2014 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10316/44054 https://doi.org/10.1007/s10485-013-9344-5 |
Resumo: | In this paper we study a generalization of the notion of categorical semidirect product, as defined in [6], to a non-protomodular context of categories where internal actions are induced by points, like in any pointed variety. There we define semidirect products only for regular points, in the sense we explain below, provided the Split Short Five Lemma between such points holds, and we show that this is the case if the category is normal, as defined in [12]. Finally, we give an example of a category that is neither protomodular nor Mal’tsev where such generalized semidirect products exist. |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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7160 |
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Semidirect Products and Split Short Five Lemma in Normal CategoriesIn this paper we study a generalization of the notion of categorical semidirect product, as defined in [6], to a non-protomodular context of categories where internal actions are induced by points, like in any pointed variety. There we define semidirect products only for regular points, in the sense we explain below, provided the Split Short Five Lemma between such points holds, and we show that this is the case if the category is normal, as defined in [12]. Finally, we give an example of a category that is neither protomodular nor Mal’tsev where such generalized semidirect products exist.Springer2014info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10316/44054http://hdl.handle.net/10316/44054https://doi.org/10.1007/s10485-013-9344-5https://doi.org/10.1007/s10485-013-9344-5enghttps://doi.org/10.1007/s10485-013-9344-5Martins-Ferreira, NelsonMontoli, AndreaSobral, Manuelainfo: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:RCAAP2021-06-29T10:02:53Zoai:estudogeral.uc.pt:10316/44054Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:53:31.354476Repositório 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 |
Semidirect Products and Split Short Five Lemma in Normal Categories |
title |
Semidirect Products and Split Short Five Lemma in Normal Categories |
spellingShingle |
Semidirect Products and Split Short Five Lemma in Normal Categories Martins-Ferreira, Nelson |
title_short |
Semidirect Products and Split Short Five Lemma in Normal Categories |
title_full |
Semidirect Products and Split Short Five Lemma in Normal Categories |
title_fullStr |
Semidirect Products and Split Short Five Lemma in Normal Categories |
title_full_unstemmed |
Semidirect Products and Split Short Five Lemma in Normal Categories |
title_sort |
Semidirect Products and Split Short Five Lemma in Normal Categories |
author |
Martins-Ferreira, Nelson |
author_facet |
Martins-Ferreira, Nelson Montoli, Andrea Sobral, Manuela |
author_role |
author |
author2 |
Montoli, Andrea Sobral, Manuela |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
Martins-Ferreira, Nelson Montoli, Andrea Sobral, Manuela |
description |
In this paper we study a generalization of the notion of categorical semidirect product, as defined in [6], to a non-protomodular context of categories where internal actions are induced by points, like in any pointed variety. There we define semidirect products only for regular points, in the sense we explain below, provided the Split Short Five Lemma between such points holds, and we show that this is the case if the category is normal, as defined in [12]. Finally, we give an example of a category that is neither protomodular nor Mal’tsev where such generalized semidirect products exist. |
publishDate |
2014 |
dc.date.none.fl_str_mv |
2014 |
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/10316/44054 http://hdl.handle.net/10316/44054 https://doi.org/10.1007/s10485-013-9344-5 https://doi.org/10.1007/s10485-013-9344-5 |
url |
http://hdl.handle.net/10316/44054 https://doi.org/10.1007/s10485-013-9344-5 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
https://doi.org/10.1007/s10485-013-9344-5 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
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 |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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RCAAP |
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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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1799133821649551360 |