Some equivalences between homotopy and derived categories

ABSTRACT: We prove two triangle equivalences. One is the triangle equivalence between the homotopy category of the bounded below complexes of Ext-injectives objects of a closed by subobjects and co-resolving subcategory of an abelian category and the derived category of the bounded below complexes o...

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Autores:
Giraldo Salazar, Hernán Alonso
Moreno Cañadas, Agustín
Saldarriaga Ortiz, Omar Darío
Tipo de recurso:
Article of investigation
Fecha de publicación:
2015
Institución:
Universidad de Antioquia
Repositorio:
Repositorio UdeA
Idioma:
eng
OAI Identifier:
oai:bibliotecadigital.udea.edu.co:10495/30843
Acceso en línea:
https://hdl.handle.net/10495/30843
Palabra clave:
Equivalencias de homotopía
Homotopy equivalences
Teoría de homotopía
Homotopy theory
Grupos abelianos
Abelian groups
Topología algebraica
Algebraic topology
Derived category
Triangulated category
Homotopy category
Auto-orthogonal category
Rights
openAccess
License
http://creativecommons.org/licenses/by-nc-sa/2.5/co/
id UDEA2_b0cc38ccfcbb5bb750621a2791e94e5e
oai_identifier_str oai:bibliotecadigital.udea.edu.co:10495/30843
network_acronym_str UDEA2
network_name_str Repositorio UdeA
repository_id_str
dc.title.spa.fl_str_mv Some equivalences between homotopy and derived categories
title Some equivalences between homotopy and derived categories
spellingShingle Some equivalences between homotopy and derived categories
Equivalencias de homotopía
Homotopy equivalences
Teoría de homotopía
Homotopy theory
Grupos abelianos
Abelian groups
Topología algebraica
Algebraic topology
Derived category
Triangulated category
Homotopy category
Auto-orthogonal category
title_short Some equivalences between homotopy and derived categories
title_full Some equivalences between homotopy and derived categories
title_fullStr Some equivalences between homotopy and derived categories
title_full_unstemmed Some equivalences between homotopy and derived categories
title_sort Some equivalences between homotopy and derived categories
dc.creator.fl_str_mv Giraldo Salazar, Hernán Alonso
Moreno Cañadas, Agustín
Saldarriaga Ortiz, Omar Darío
dc.contributor.author.none.fl_str_mv Giraldo Salazar, Hernán Alonso
Moreno Cañadas, Agustín
Saldarriaga Ortiz, Omar Darío
dc.subject.lemb.none.fl_str_mv Equivalencias de homotopía
Homotopy equivalences
Teoría de homotopía
Homotopy theory
Grupos abelianos
Abelian groups
Topología algebraica
Algebraic topology
topic Equivalencias de homotopía
Homotopy equivalences
Teoría de homotopía
Homotopy theory
Grupos abelianos
Abelian groups
Topología algebraica
Algebraic topology
Derived category
Triangulated category
Homotopy category
Auto-orthogonal category
dc.subject.proposal.spa.fl_str_mv Derived category
Triangulated category
Homotopy category
Auto-orthogonal category
description ABSTRACT: We prove two triangle equivalences. One is the triangle equivalence between the homotopy category of the bounded below complexes of Ext-injectives objects of a closed by subobjects and co-resolving subcategory of an abelian category and the derived category of the bounded below complexes over The other triangle equivalence is between the homotopy category of the bounded cohomology and bounded below complexes over a strongly closed by cokernels of monomorphisms and auto-orthogonal subcategory of an abelian category and the derived category of the bounded cohomology and bounded below complexes over
publishDate 2015
dc.date.issued.none.fl_str_mv 2015
dc.date.accessioned.none.fl_str_mv 2022-09-25T00:49:47Z
dc.date.available.none.fl_str_mv 2022-09-25T00:49:47Z
dc.type.spa.fl_str_mv info:eu-repo/semantics/article
dc.type.coarversion.fl_str_mv http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.hasversion.spa.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.coar.spa.fl_str_mv http://purl.org/coar/resource_type/c_2df8fbb1
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dc.type.local.spa.fl_str_mv Artículo de investigación
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status_str publishedVersion
dc.identifier.issn.none.fl_str_mv 0972-0871
dc.identifier.uri.none.fl_str_mv https://hdl.handle.net/10495/30843
dc.identifier.doi.none.fl_str_mv 10.17654/FJMSSep2015_001_014
dc.identifier.eissn.none.fl_str_mv 0971-4332
identifier_str_mv 0972-0871
10.17654/FJMSSep2015_001_014
0971-4332
url https://hdl.handle.net/10495/30843
dc.language.iso.spa.fl_str_mv eng
language eng
dc.rights.spa.fl_str_mv info:eu-repo/semantics/openAccess
dc.rights.uri.*.fl_str_mv http://creativecommons.org/licenses/by-nc-sa/2.5/co/
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dc.rights.creativecommons.spa.fl_str_mv https://creativecommons.org/licenses/by-nc-sa/4.0/
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc-sa/2.5/co/
http://purl.org/coar/access_right/c_abf2
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dc.format.extent.spa.fl_str_mv 14
dc.format.mimetype.spa.fl_str_mv application/pdf
dc.publisher.spa.fl_str_mv Universidad de Allahabad
dc.publisher.group.spa.fl_str_mv Álgebra Teoría de Números y Aplicaciones: ERM
Álgebra U de A
dc.publisher.place.spa.fl_str_mv Allahabad, India
institution Universidad de Antioquia
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spelling Giraldo Salazar, Hernán AlonsoMoreno Cañadas, AgustínSaldarriaga Ortiz, Omar Darío2022-09-25T00:49:47Z2022-09-25T00:49:47Z20150972-0871https://hdl.handle.net/10495/3084310.17654/FJMSSep2015_001_0140971-4332ABSTRACT: We prove two triangle equivalences. One is the triangle equivalence between the homotopy category of the bounded below complexes of Ext-injectives objects of a closed by subobjects and co-resolving subcategory of an abelian category and the derived category of the bounded below complexes over The other triangle equivalence is between the homotopy category of the bounded cohomology and bounded below complexes over a strongly closed by cokernels of monomorphisms and auto-orthogonal subcategory of an abelian category and the derived category of the bounded cohomology and bounded below complexes overCOL0086896COL001721714application/pdfengUniversidad de AllahabadÁlgebra Teoría de Números y Aplicaciones: ERMÁlgebra U de AAllahabad, Indiainfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_2df8fbb1https://purl.org/redcol/resource_type/ARTArtículo de investigaciónhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-sa/2.5/co/http://purl.org/coar/access_right/c_abf2https://creativecommons.org/licenses/by-nc-sa/4.0/Some equivalences between homotopy and derived categoriesEquivalencias de homotopíaHomotopy equivalencesTeoría de homotopíaHomotopy theoryGrupos abelianosAbelian groupsTopología algebraicaAlgebraic topologyDerived categoryTriangulated categoryHomotopy categoryAuto-orthogonal categoryFar East Journal of Mathematical Sciences114981ORIGINALGiraldoHernan_2015_SomeEquivalencesBetween .pdfGiraldoHernan_2015_SomeEquivalencesBetween .pdfArtículo de investigaciónapplication/pdf122392https://bibliotecadigital.udea.edu.co/bitstream/10495/30843/1/GiraldoHernan_2015_SomeEquivalencesBetween%20.pdf32ada6c16bfb793ecaadc00e1dd57fd2MD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-81051https://bibliotecadigital.udea.edu.co/bitstream/10495/30843/2/license_rdfe2060682c9c70d4d30c83c51448f4eedMD52LICENSElicense.txtlicense.txttext/plain; charset=utf-81748https://bibliotecadigital.udea.edu.co/bitstream/10495/30843/3/license.txt8a4605be74aa9ea9d79846c1fba20a33MD5310495/30843oai:bibliotecadigital.udea.edu.co:10495/308432022-09-24 19:49:48.037Repositorio Institucional Universidad de Antioquiaandres.perez@udea.edu.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