Pointed homotopy of maps between 2-crossed modules of commutative algebras

Detalhes bibliográficos
Autor(a) principal: Akça, I. Ilker
Data de Publicação: 2016
Outros Autores: Emir, Kadir, Martins, João Faria
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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spelling 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
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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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