Publicação
Topological protomodular algebras
| 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. |
|---|---|
| Autores principais: | Borceux, F. |
| Outros Autores: | Clementino, Maria Manuel |
| Assunto: | Topological algebra Algebraic theory Protomodular category |
| Ano: | 2006 |
| País: | Portugal |
| Tipo de documento: | artigo |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade de Coimbra |
| Idioma: | inglês |
| Origem: | Estudo Geral - Universidade de Coimbra |
| _version_ | 1868416269831634944 |
|---|---|
| author | Borceux, F. |
| author2 | Clementino, Maria Manuel |
| author2_role | author |
| author_facet | Borceux, F. Clementino, Maria Manuel |
| author_role | author |
| country_str | PT |
| creators_json_txt | [{\"Person.name\":\"Borceux, F.\"},{\"Person.name\":\"Clementino, Maria Manuel\"}] |
| datacite.creators.creator.creatorName.fl_str_mv | Borceux, F. Clementino, Maria Manuel |
| datacite.rights.fl_str_mv | http://purl.org/coar/access_right/c_abf2 |
| datacite.subjects.subject.fl_str_mv | Topological algebra Algebraic theory Protomodular category |
| datacite.titles.title.fl_str_mv | Topological protomodular algebras |
| dc.creator.none.fl_str_mv | Borceux, F. Clementino, Maria Manuel |
| dc.description.none.fl_str_mv | http://www.sciencedirect.com/science/article/B6V1K-4GXVG0K-2/1/80524f4470b30ebfaf37012e4d8b45dc |
| dc.format.none.fl_str_mv | aplication/PDF |
| dc.identifier.none.fl_str_mv | https://hdl.handle.net/10316/4613 |
| dc.language.none.fl_str_mv | eng |
| dc.rights.none.fl_str_mv | http://purl.org/coar/access_right/c_abf2 |
| dc.subject.none.fl_str_mv | Topological algebra Algebraic theory Protomodular category |
| dc.title.fl_str_mv | Topological protomodular algebras |
| dc.type.none.fl_str_mv | http://purl.org/coar/resource_type/c_6501 |
| 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. |
| dirty | 0 |
| eu_rights_str_mv | openAccess |
| format | article |
| id | estudogl_149294cfcaf4dec045810afa42e052d5 |
| identifier.url.fl_str_mv | https://hdl.handle.net/10316/4613 |
| instacron_str | uc |
| institution | Universidade de Coimbra |
| instname_str | Universidade de Coimbra |
| language | eng |
| network_acronym_str | estudogl |
| network_name_str | Estudo Geral - Universidade de Coimbra |
| oai_identifier_str | oai:estudogeral.uc.pt:10316/4613 |
| organization_str_mv | urn:organizationAcronym:uc |
| person_str_mv | Borceux, F. Clementino, Maria Manuel |
| publishDate | 2006 |
| reponame_str | Estudo Geral - Universidade de Coimbra |
| repository_id_str | urn:repositoryAcronym:estudogl |
| service_str_mv | urn:repositoryAcronym:estudogl |
| spelling | Topological protomodular algebrasBorceux, F.Clementino, Maria ManuelTopological algebraAlgebraic theoryProtomodular categoryopen accesshttp://purl.org/coar/access_right/c_abf2https://hdl.handle.net/10316/4613HandleTopology and its Applications. 153:16 (2006) 3085-3100N/AHasVersionhttps://hdl.handle.net/10316/4613Handlehttps://doi.org/10.1016/j.topol.2004.12.010DOI2006Topological 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-2/1/80524f4470b30ebfaf37012e4d8b45dcengaplication/PDFjournal articlehttp://purl.org/coar/resource_type/c_6501literature |
| spellingShingle | Topological protomodular algebras Borceux, F. Topological algebra Algebraic theory Protomodular category |
| status | SINGLETON |
| subject.fl_str_mv | Topological algebra Algebraic theory Protomodular category |
| title | Topological protomodular algebras |
| title_full | Topological protomodular algebras |
| title_fullStr | Topological protomodular algebras |
| title_full_unstemmed | Topological protomodular algebras |
| title_short | Topological protomodular algebras |
| title_sort | Topological protomodular algebras |
| topic | Topological algebra Algebraic theory Protomodular category |
| topic_facet | Topological algebra Algebraic theory Protomodular category |
| url | https://hdl.handle.net/10316/4613 |
| visible | 1 |