Higher central extensions and cohomology
| Autor(a) principal: | |
|---|---|
| Data de Publicação: | 2015 |
| 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/10316/43872 https://doi.org/10.1016/j.aim.2015.09.023 |
Resumo: | We establish a Galois-theoretic interpretation of cohomology in semi-abelian categories: cohomology with trivial coefficients classifies central extensions, also in arbitrarily high degrees. This allows us to obtain a duality, in a certain sense, between "internal" homology and "external" cohomology in semi-abelian categories. These results depend on a geometric viewpoint of the concept of a higher central extension, as well as the algebraic one in terms of commutators. |
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Higher central extensions and cohomologyWe establish a Galois-theoretic interpretation of cohomology in semi-abelian categories: cohomology with trivial coefficients classifies central extensions, also in arbitrarily high degrees. This allows us to obtain a duality, in a certain sense, between "internal" homology and "external" cohomology in semi-abelian categories. These results depend on a geometric viewpoint of the concept of a higher central extension, as well as the algebraic one in terms of commutators.Elsevier2015-02-18info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10316/43872http://hdl.handle.net/10316/43872https://doi.org/10.1016/j.aim.2015.09.023https://doi.org/10.1016/j.aim.2015.09.023enghttp://www.sciencedirect.com/science/article/pii/S0001870815003643Rodelo, DianaVan der Linden, Timinfo: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:RCAAP2021-06-29T10:02:56Zoai:estudogeral.uc.pt:10316/43872Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:53:29.450890Repositório 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 |
Higher central extensions and cohomology |
| title |
Higher central extensions and cohomology |
| spellingShingle |
Higher central extensions and cohomology Rodelo, Diana |
| title_short |
Higher central extensions and cohomology |
| title_full |
Higher central extensions and cohomology |
| title_fullStr |
Higher central extensions and cohomology |
| title_full_unstemmed |
Higher central extensions and cohomology |
| title_sort |
Higher central extensions and cohomology |
| author |
Rodelo, Diana |
| author_facet |
Rodelo, Diana Van der Linden, Tim |
| author_role |
author |
| author2 |
Van der Linden, Tim |
| author2_role |
author |
| dc.contributor.author.fl_str_mv |
Rodelo, Diana Van der Linden, Tim |
| description |
We establish a Galois-theoretic interpretation of cohomology in semi-abelian categories: cohomology with trivial coefficients classifies central extensions, also in arbitrarily high degrees. This allows us to obtain a duality, in a certain sense, between "internal" homology and "external" cohomology in semi-abelian categories. These results depend on a geometric viewpoint of the concept of a higher central extension, as well as the algebraic one in terms of commutators. |
| publishDate |
2015 |
| dc.date.none.fl_str_mv |
2015-02-18 |
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info:eu-repo/semantics/publishedVersion |
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info:eu-repo/semantics/article |
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article |
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publishedVersion |
| dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10316/43872 http://hdl.handle.net/10316/43872 https://doi.org/10.1016/j.aim.2015.09.023 https://doi.org/10.1016/j.aim.2015.09.023 |
| url |
http://hdl.handle.net/10316/43872 https://doi.org/10.1016/j.aim.2015.09.023 |
| dc.language.iso.fl_str_mv |
eng |
| language |
eng |
| dc.relation.none.fl_str_mv |
http://www.sciencedirect.com/science/article/pii/S0001870815003643 |
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info:eu-repo/semantics/openAccess |
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openAccess |
| dc.publisher.none.fl_str_mv |
Elsevier |
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Elsevier |
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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 |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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1799133821602365440 |