Pointed homotopy of maps between 2-crossed modules of commutative algebras
Autor(a) principal: | |
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Data de Publicação: | 2016 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | https://doi.org/10.4310/HHA.2016.V18.N1.A6 |
Resumo: | JFM was partially supported by CMA/FCT/UNL, under the project UID/MAT/00297/2013 and by FCT (Portugal) through the "Geometry and Mathematical Physics Project", FCT EXCL/MATGEO/0222/2012. KE expresses his gratitude to CMA for the hospitality in 2014/15. We would like to thank Ronald Brown for useful comments and several corrections. |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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7160 |
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Pointed homotopy of maps between 2-crossed modules of commutative algebras2-crossed module of commutative algebrasCrossed module of commutative algebrasQuadratic derivationSimplicial commutative algebraMathematics (miscellaneous)JFM was partially supported by CMA/FCT/UNL, under the project UID/MAT/00297/2013 and by FCT (Portugal) through the "Geometry and Mathematical Physics Project", FCT EXCL/MATGEO/0222/2012. KE expresses his gratitude to CMA for the hospitality in 2014/15. We would like to thank Ronald Brown for useful comments and several corrections.We address the homotopy theory of 2-crossed modules of commutative algebras, which are equivalent to simplicial commutative algebras with Moore complex of length two. In particular, we construct for maps of 2-crossed modules a homotopy relation, and prove that it yields an equivalence relation in very unrestricted cases (freeness up to order one of the domain 2-crossed module). This latter condition strictly includes the case when the domain is cofibrant. Furthermore, we prove that this notion of homotopy yields a groupoid with objects being the 2-crossed module maps between two fixed 2-crossed modules (with free up to order one domain), the morphisms being the homotopies between 2-crossed module maps.DM - Departamento de MatemáticaCMA - Centro de Matemática e AplicaçõesRUNAkça, I. IlkerEmir, KadirMartins, João Faria2018-07-19T22:11:57Z20162016-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article30application/pdfhttps://doi.org/10.4310/HHA.2016.V18.N1.A6eng1532-0073PURE: 5465365http://www.scopus.com/inward/record.url?scp=85046671254&partnerID=8YFLogxKhttps://doi.org/10.4310/HHA.2016.V18.N1.A6info: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:RCAAP2024-03-11T04:22:42Zoai:run.unl.pt:10362/42040Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:31:26.315911Repositório 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 |
Pointed homotopy of maps between 2-crossed modules of commutative algebras |
title |
Pointed homotopy of maps between 2-crossed modules of commutative algebras |
spellingShingle |
Pointed homotopy of maps between 2-crossed modules of commutative algebras Akça, I. Ilker 2-crossed module of commutative algebras Crossed module of commutative algebras Quadratic derivation Simplicial commutative algebra Mathematics (miscellaneous) |
title_short |
Pointed homotopy of maps between 2-crossed modules of commutative algebras |
title_full |
Pointed homotopy of maps between 2-crossed modules of commutative algebras |
title_fullStr |
Pointed homotopy of maps between 2-crossed modules of commutative algebras |
title_full_unstemmed |
Pointed homotopy of maps between 2-crossed modules of commutative algebras |
title_sort |
Pointed homotopy of maps between 2-crossed modules of commutative algebras |
author |
Akça, I. Ilker |
author_facet |
Akça, I. Ilker Emir, Kadir Martins, João Faria |
author_role |
author |
author2 |
Emir, Kadir Martins, João Faria |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
DM - Departamento de Matemática CMA - Centro de Matemática e Aplicações RUN |
dc.contributor.author.fl_str_mv |
Akça, I. Ilker Emir, Kadir Martins, João Faria |
dc.subject.por.fl_str_mv |
2-crossed module of commutative algebras Crossed module of commutative algebras Quadratic derivation Simplicial commutative algebra Mathematics (miscellaneous) |
topic |
2-crossed module of commutative algebras Crossed module of commutative algebras Quadratic derivation Simplicial commutative algebra Mathematics (miscellaneous) |
description |
JFM was partially supported by CMA/FCT/UNL, under the project UID/MAT/00297/2013 and by FCT (Portugal) through the "Geometry and Mathematical Physics Project", FCT EXCL/MATGEO/0222/2012. KE expresses his gratitude to CMA for the hospitality in 2014/15. We would like to thank Ronald Brown for useful comments and several corrections. |
publishDate |
2016 |
dc.date.none.fl_str_mv |
2016 2016-01-01T00:00:00Z 2018-07-19T22:11:57Z |
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 |
https://doi.org/10.4310/HHA.2016.V18.N1.A6 |
url |
https://doi.org/10.4310/HHA.2016.V18.N1.A6 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
1532-0073 PURE: 5465365 http://www.scopus.com/inward/record.url?scp=85046671254&partnerID=8YFLogxK https://doi.org/10.4310/HHA.2016.V18.N1.A6 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
30 application/pdf |
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 |
repository.mail.fl_str_mv |
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1799137937936351232 |