Universal coefficient theorem in triangulated categories

Autores
Pirashvili, Teimuraz; Redondo, Maria Julia
Año de publicación
2008
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We consider a homology theory Open image in new window on a triangulated category Open image in new window with values in an abelian category Open image in new window . If the functor h reflects isomorphisms, is full and is such that for any object x in Open image in new window there is an object X in Open image in new window with an isomorphism between h(X) and x, we prove that Open image in new window is a hereditary abelian category, all idempotents in Open image in new window split and the kernel of h is a square zero ideal which as a bifunctor on Open image in new window is isomorphic to Open image in new window.
Fil: Pirashvili, Teimuraz. University of Leicester; Reino Unido
Fil: Redondo, Maria Julia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina
Materia
Abelian Category
Homology Theory
Triangulated Category
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/79648
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Universal coefficient theorem in triangulated categoriesPirashvili, TeimurazRedondo, Maria JuliaAbelian CategoryHomology TheoryTriangulated Categoryhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We consider a homology theory Open image in new window on a triangulated category Open image in new window with values in an abelian category Open image in new window . If the functor h reflects isomorphisms, is full and is such that for any object x in Open image in new window there is an object X in Open image in new window with an isomorphism between h(X) and x, we prove that Open image in new window is a hereditary abelian category, all idempotents in Open image in new window split and the kernel of h is a square zero ideal which as a bifunctor on Open image in new window is isomorphic to Open image in new window.Fil: Pirashvili, Teimuraz. University of Leicester; Reino UnidoFil: Redondo, Maria Julia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; ArgentinaSpringer Verlag Berlín2008-04info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/79648Pirashvili, Teimuraz; Redondo, Maria Julia; Universal coefficient theorem in triangulated categories; Springer Verlag Berlín; Algebras and Representation Theory; 11; 2; 4-2008; 107-1141386-923X1572-9079CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s10468-007-9077-yinfo:eu-repo/semantics/altIdentifier/doi/10.1007/s10468-007-9077-yinfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/math/0604412info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:44:09Zoai:ri.conicet.gov.ar:11336/79648instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-22 11:44:09.919CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Universal coefficient theorem in triangulated categories
title Universal coefficient theorem in triangulated categories
spellingShingle Universal coefficient theorem in triangulated categories
Pirashvili, Teimuraz
Abelian Category
Homology Theory
Triangulated Category
title_short Universal coefficient theorem in triangulated categories
title_full Universal coefficient theorem in triangulated categories
title_fullStr Universal coefficient theorem in triangulated categories
title_full_unstemmed Universal coefficient theorem in triangulated categories
title_sort Universal coefficient theorem in triangulated categories
dc.creator.none.fl_str_mv Pirashvili, Teimuraz
Redondo, Maria Julia
author Pirashvili, Teimuraz
author_facet Pirashvili, Teimuraz
Redondo, Maria Julia
author_role author
author2 Redondo, Maria Julia
author2_role author
dc.subject.none.fl_str_mv Abelian Category
Homology Theory
Triangulated Category
topic Abelian Category
Homology Theory
Triangulated Category
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We consider a homology theory Open image in new window on a triangulated category Open image in new window with values in an abelian category Open image in new window . If the functor h reflects isomorphisms, is full and is such that for any object x in Open image in new window there is an object X in Open image in new window with an isomorphism between h(X) and x, we prove that Open image in new window is a hereditary abelian category, all idempotents in Open image in new window split and the kernel of h is a square zero ideal which as a bifunctor on Open image in new window is isomorphic to Open image in new window.
Fil: Pirashvili, Teimuraz. University of Leicester; Reino Unido
Fil: Redondo, Maria Julia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina
description We consider a homology theory Open image in new window on a triangulated category Open image in new window with values in an abelian category Open image in new window . If the functor h reflects isomorphisms, is full and is such that for any object x in Open image in new window there is an object X in Open image in new window with an isomorphism between h(X) and x, we prove that Open image in new window is a hereditary abelian category, all idempotents in Open image in new window split and the kernel of h is a square zero ideal which as a bifunctor on Open image in new window is isomorphic to Open image in new window.
publishDate 2008
dc.date.none.fl_str_mv 2008-04
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/79648
Pirashvili, Teimuraz; Redondo, Maria Julia; Universal coefficient theorem in triangulated categories; Springer Verlag Berlín; Algebras and Representation Theory; 11; 2; 4-2008; 107-114
1386-923X
1572-9079
CONICET Digital
CONICET
url http://hdl.handle.net/11336/79648
identifier_str_mv Pirashvili, Teimuraz; Redondo, Maria Julia; Universal coefficient theorem in triangulated categories; Springer Verlag Berlín; Algebras and Representation Theory; 11; 2; 4-2008; 107-114
1386-923X
1572-9079
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s10468-007-9077-y
info:eu-repo/semantics/altIdentifier/doi/10.1007/s10468-007-9077-y
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/math/0604412
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer Verlag Berlín
publisher.none.fl_str_mv Springer Verlag Berlín
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 12.982451

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