Topological protomodular algebras

Detalhes bibliográficos
Autor(a) principal: Borceux, F.
Data de Publicação: 2006
Outros Autores: Clementino, Maria Manuel
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10316/4613
https://doi.org/10.1016/j.topol.2004.12.010
Resumo: Topological groups have very striking properties, which have already been generalized to weaker "group like" structures, like various kinds of loops. This paper intends to show evidence that this generalization holds for a much wider class of theories, known as the protomodular theories, and which admit both an elegant categorical characterization and an easy description in universal algebra terms. Thus we propose a synthetic approach which allows to prove in a unique framework that the most striking properties of topological groups hold as well for loops or even semi-loops, rings with or without unit, associative algebras with or without unit, Lie algebras, Jordan algebras, Boolean algebras, Heyting algebras, Boolean rings, Heyting semi-lattices, and so on.
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spelling Topological protomodular algebrasTopological algebraAlgebraic theoryProtomodular categoryTopological groups have very striking properties, which have already been generalized to weaker "group like" structures, like various kinds of loops. This paper intends to show evidence that this generalization holds for a much wider class of theories, known as the protomodular theories, and which admit both an elegant categorical characterization and an easy description in universal algebra terms. Thus we propose a synthetic approach which allows to prove in a unique framework that the most striking properties of topological groups hold as well for loops or even semi-loops, rings with or without unit, associative algebras with or without unit, Lie algebras, Jordan algebras, Boolean algebras, Heyting algebras, Boolean rings, Heyting semi-lattices, and so on.http://www.sciencedirect.com/science/article/B6V1K-4GXVG0K-2/1/80524f4470b30ebfaf37012e4d8b45dc2006info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleaplication/PDFhttp://hdl.handle.net/10316/4613http://hdl.handle.net/10316/4613https://doi.org/10.1016/j.topol.2004.12.010engTopology and its Applications. 153:16 (2006) 3085-3100Borceux, F.Clementino, Maria Manuelinfo: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:RCAAP2020-11-06T16:59:23Zoai:estudogeral.uc.pt:10316/4613Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T21:00:41.598672Repositório 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 Topological protomodular algebras
title Topological protomodular algebras
spellingShingle Topological protomodular algebras
Borceux, F.
Topological algebra
Algebraic theory
Protomodular category
title_short Topological protomodular algebras
title_full Topological protomodular algebras
title_fullStr Topological protomodular algebras
title_full_unstemmed Topological protomodular algebras
title_sort Topological protomodular algebras
author Borceux, F.
author_facet Borceux, F.
Clementino, Maria Manuel
author_role author
author2 Clementino, Maria Manuel
author2_role author
dc.contributor.author.fl_str_mv Borceux, F.
Clementino, Maria Manuel
dc.subject.por.fl_str_mv Topological algebra
Algebraic theory
Protomodular category
topic Topological algebra
Algebraic theory
Protomodular category
description Topological groups have very striking properties, which have already been generalized to weaker "group like" structures, like various kinds of loops. This paper intends to show evidence that this generalization holds for a much wider class of theories, known as the protomodular theories, and which admit both an elegant categorical characterization and an easy description in universal algebra terms. Thus we propose a synthetic approach which allows to prove in a unique framework that the most striking properties of topological groups hold as well for loops or even semi-loops, rings with or without unit, associative algebras with or without unit, Lie algebras, Jordan algebras, Boolean algebras, Heyting algebras, Boolean rings, Heyting semi-lattices, and so on.
publishDate 2006
dc.date.none.fl_str_mv 2006
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dc.identifier.uri.fl_str_mv http://hdl.handle.net/10316/4613
http://hdl.handle.net/10316/4613
https://doi.org/10.1016/j.topol.2004.12.010
url http://hdl.handle.net/10316/4613
https://doi.org/10.1016/j.topol.2004.12.010
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Topology and its Applications. 153:16 (2006) 3085-3100
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