On $2$-star-permutability in regular multi-pointed categories

Detalhes bibliográficos
Autor(a) principal: Gran, Marino
Data de Publicação: 2014
Outros Autores: Rodelo, Diana
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10316/43922
https://doi.org/10.1142/S0219498814500686
Resumo: $2$-star-permutable categories were introduced in a joint work with Z. Janelidze and A. Ursini as a common generalisation of regular Mal'tsev categories and of normal subtractive categories. In the present article we first characterise these categories in terms of what we call star-regular pushouts. We then show that the $3 \times 3$ Lemma characterising normal subtractive categories and the Cuboid Lemma characterising regular Mal'tsev categories are special instances of a more general homological lemma for star-exact sequences. We prove that $2$-star-permutability is equivalent to the validity of this lemma for a star-regular category.
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spelling On $2$-star-permutability in regular multi-pointed categories$2$-star-permutable categories were introduced in a joint work with Z. Janelidze and A. Ursini as a common generalisation of regular Mal'tsev categories and of normal subtractive categories. In the present article we first characterise these categories in terms of what we call star-regular pushouts. We then show that the $3 \times 3$ Lemma characterising normal subtractive categories and the Cuboid Lemma characterising regular Mal'tsev categories are special instances of a more general homological lemma for star-exact sequences. We prove that $2$-star-permutability is equivalent to the validity of this lemma for a star-regular category.World Scientific Publishing2014info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10316/43922http://hdl.handle.net/10316/43922https://doi.org/10.1142/S0219498814500686https://doi.org/10.1142/S0219498814500686enghttp://www.worldscientific.com/doi/pdfplus/10.1142/S0219498814500686Gran, MarinoRodelo, Dianainfo: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:RCAAP2021-06-29T10:03:20Zoai:estudogeral.uc.pt:10316/43922Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:53:30.518484Repositório 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 On $2$-star-permutability in regular multi-pointed categories
title On $2$-star-permutability in regular multi-pointed categories
spellingShingle On $2$-star-permutability in regular multi-pointed categories
Gran, Marino
title_short On $2$-star-permutability in regular multi-pointed categories
title_full On $2$-star-permutability in regular multi-pointed categories
title_fullStr On $2$-star-permutability in regular multi-pointed categories
title_full_unstemmed On $2$-star-permutability in regular multi-pointed categories
title_sort On $2$-star-permutability in regular multi-pointed categories
author Gran, Marino
author_facet Gran, Marino
Rodelo, Diana
author_role author
author2 Rodelo, Diana
author2_role author
dc.contributor.author.fl_str_mv Gran, Marino
Rodelo, Diana
description $2$-star-permutable categories were introduced in a joint work with Z. Janelidze and A. Ursini as a common generalisation of regular Mal'tsev categories and of normal subtractive categories. In the present article we first characterise these categories in terms of what we call star-regular pushouts. We then show that the $3 \times 3$ Lemma characterising normal subtractive categories and the Cuboid Lemma characterising regular Mal'tsev categories are special instances of a more general homological lemma for star-exact sequences. We prove that $2$-star-permutability is equivalent to the validity of this lemma for a star-regular category.
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/10316/43922
http://hdl.handle.net/10316/43922
https://doi.org/10.1142/S0219498814500686
https://doi.org/10.1142/S0219498814500686
url http://hdl.handle.net/10316/43922
https://doi.org/10.1142/S0219498814500686
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv http://www.worldscientific.com/doi/pdfplus/10.1142/S0219498814500686
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv World Scientific Publishing
publisher.none.fl_str_mv World Scientific Publishing
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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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
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