Variations of the Shifting Lemma and Goursat categories
Autor(a) principal: | |
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Data de Publicação: | 2019 |
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/10400.1/14408 |
Resumo: | We prove that Mal'tsev and Goursat categories may be characterized through variations of the Shifting Lemma, that is classically expressed in terms of three congruences R, S and T, and characterizes congruence modular varieties. We first show that a regular category C is a Mal'tsev category if and only if the Shifting Lemma holds for reflexive relations on the same object in C. Moreover, we prove that a regular category C is a Goursat category if and only if the Shifting Lemma holds for a reflexive relation S and reflexive and positive relations R and T in C. In particular this provides a new characterization of 2-permutable and 3-permutable varieties and quasi-varieties of universal algebras. |
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Variations of the Shifting Lemma and Goursat categoriesMal'tsev categoriesCategoriesShifting LemmaCongruence modular varieties3-permutable varietiesWe prove that Mal'tsev and Goursat categories may be characterized through variations of the Shifting Lemma, that is classically expressed in terms of three congruences R, S and T, and characterizes congruence modular varieties. We first show that a regular category C is a Mal'tsev category if and only if the Shifting Lemma holds for reflexive relations on the same object in C. Moreover, we prove that a regular category C is a Goursat category if and only if the Shifting Lemma holds for a reflexive relation S and reflexive and positive relations R and T in C. In particular this provides a new characterization of 2-permutable and 3-permutable varieties and quasi-varieties of universal algebras.European Regional Development FundEuropean Union (EU)Fonds de la Recherche Scientifique-FNRS Credit Bref Sejour a l'etrangerFonds de la Recherche Scientifique - FNRS [2018/V 3/5/033-IB/JN-11440]Springer Basel AgSapientiaGran, MarinoRodelo, DianaNguefeu, Idriss Tchoffo2020-07-24T10:52:48Z2019-032019-03-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.1/14408eng0002-524010.1007/s00012-018-0575-zinfo: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:RCAAP2023-07-24T10:26:42Zoai:sapientia.ualg.pt:10400.1/14408Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:05:24.941408Repositório 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 |
Variations of the Shifting Lemma and Goursat categories |
title |
Variations of the Shifting Lemma and Goursat categories |
spellingShingle |
Variations of the Shifting Lemma and Goursat categories Gran, Marino Mal'tsev categories Categories Shifting Lemma Congruence modular varieties 3-permutable varieties |
title_short |
Variations of the Shifting Lemma and Goursat categories |
title_full |
Variations of the Shifting Lemma and Goursat categories |
title_fullStr |
Variations of the Shifting Lemma and Goursat categories |
title_full_unstemmed |
Variations of the Shifting Lemma and Goursat categories |
title_sort |
Variations of the Shifting Lemma and Goursat categories |
author |
Gran, Marino |
author_facet |
Gran, Marino Rodelo, Diana Nguefeu, Idriss Tchoffo |
author_role |
author |
author2 |
Rodelo, Diana Nguefeu, Idriss Tchoffo |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
Sapientia |
dc.contributor.author.fl_str_mv |
Gran, Marino Rodelo, Diana Nguefeu, Idriss Tchoffo |
dc.subject.por.fl_str_mv |
Mal'tsev categories Categories Shifting Lemma Congruence modular varieties 3-permutable varieties |
topic |
Mal'tsev categories Categories Shifting Lemma Congruence modular varieties 3-permutable varieties |
description |
We prove that Mal'tsev and Goursat categories may be characterized through variations of the Shifting Lemma, that is classically expressed in terms of three congruences R, S and T, and characterizes congruence modular varieties. We first show that a regular category C is a Mal'tsev category if and only if the Shifting Lemma holds for reflexive relations on the same object in C. Moreover, we prove that a regular category C is a Goursat category if and only if the Shifting Lemma holds for a reflexive relation S and reflexive and positive relations R and T in C. In particular this provides a new characterization of 2-permutable and 3-permutable varieties and quasi-varieties of universal algebras. |
publishDate |
2019 |
dc.date.none.fl_str_mv |
2019-03 2019-03-01T00:00:00Z 2020-07-24T10:52:48Z |
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/10400.1/14408 |
url |
http://hdl.handle.net/10400.1/14408 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
0002-5240 10.1007/s00012-018-0575-z |
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 Basel Ag |
publisher.none.fl_str_mv |
Springer Basel Ag |
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 |
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1799133294050148352 |