Homotopy colimits of diagrams over posets and variations on a theorem of Thomason

Autores
Fernández, Ximena Laura; Minian, Elias Gabriel
Año de publicación
2016
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We use a classical result of McCord and reduction methods of finite spaces to prove a generalization of Thomason's theorem on homotopy colimits over posets. In particular, this allows us to characterize the homotopy colimits of diagrams of simplicial complexes in terms of the Grothendieck construction on the diagrams of their face posets. We also derive analogues of well known results on homotopy colimits in the combinatorial setting, including a cofinality theorem and a generalization of Quillen's Theorem A for posets.
Fil: Fernández, Ximena Laura. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; Argentina
Fil: Minian, Elias Gabriel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; Argentina
Materia
FINITE TOPOLOGICAL SPACE
GROTHENDIECK CONSTRUCTION
HOMOTOPY COLIMIT
POSET
QUILLEN'S THEOREM A
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:11336/55511
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Homotopy colimits of diagrams over posets and variations on a theorem of ThomasonFernández, Ximena LauraMinian, Elias GabrielFINITE TOPOLOGICAL SPACEGROTHENDIECK CONSTRUCTIONHOMOTOPY COLIMITPOSETQUILLEN'S THEOREM Ahttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We use a classical result of McCord and reduction methods of finite spaces to prove a generalization of Thomason's theorem on homotopy colimits over posets. In particular, this allows us to characterize the homotopy colimits of diagrams of simplicial complexes in terms of the Grothendieck construction on the diagrams of their face posets. We also derive analogues of well known results on homotopy colimits in the combinatorial setting, including a cofinality theorem and a generalization of Quillen's Theorem A for posets.Fil: Fernández, Ximena Laura. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; ArgentinaFil: Minian, Elias Gabriel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; ArgentinaInternational Press Boston2016-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/55511Fernández, Ximena Laura; Minian, Elias Gabriel; Homotopy colimits of diagrams over posets and variations on a theorem of Thomason; International Press Boston; Homology, Homotopy And Applications (hha); 18; 2; 1-2016; 233-2451532-0073CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1407.5646info:eu-repo/semantics/altIdentifier/doi/10.4310/HHA.2016.v18.n2.a13info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:48:35Zoai:ri.conicet.gov.ar:11336/55511instacron: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:34982025-09-03 09:48:36.159CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Homotopy colimits of diagrams over posets and variations on a theorem of Thomason
title Homotopy colimits of diagrams over posets and variations on a theorem of Thomason
spellingShingle Homotopy colimits of diagrams over posets and variations on a theorem of Thomason
Fernández, Ximena Laura
FINITE TOPOLOGICAL SPACE
GROTHENDIECK CONSTRUCTION
HOMOTOPY COLIMIT
POSET
QUILLEN'S THEOREM A
title_short Homotopy colimits of diagrams over posets and variations on a theorem of Thomason
title_full Homotopy colimits of diagrams over posets and variations on a theorem of Thomason
title_fullStr Homotopy colimits of diagrams over posets and variations on a theorem of Thomason
title_full_unstemmed Homotopy colimits of diagrams over posets and variations on a theorem of Thomason
title_sort Homotopy colimits of diagrams over posets and variations on a theorem of Thomason
dc.creator.none.fl_str_mv Fernández, Ximena Laura
Minian, Elias Gabriel
author Fernández, Ximena Laura
author_facet Fernández, Ximena Laura
Minian, Elias Gabriel
author_role author
author2 Minian, Elias Gabriel
author2_role author
dc.subject.none.fl_str_mv FINITE TOPOLOGICAL SPACE
GROTHENDIECK CONSTRUCTION
HOMOTOPY COLIMIT
POSET
QUILLEN'S THEOREM A
topic FINITE TOPOLOGICAL SPACE
GROTHENDIECK CONSTRUCTION
HOMOTOPY COLIMIT
POSET
QUILLEN'S THEOREM A
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 use a classical result of McCord and reduction methods of finite spaces to prove a generalization of Thomason's theorem on homotopy colimits over posets. In particular, this allows us to characterize the homotopy colimits of diagrams of simplicial complexes in terms of the Grothendieck construction on the diagrams of their face posets. We also derive analogues of well known results on homotopy colimits in the combinatorial setting, including a cofinality theorem and a generalization of Quillen's Theorem A for posets.
Fil: Fernández, Ximena Laura. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; Argentina
Fil: Minian, Elias Gabriel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; Argentina
description We use a classical result of McCord and reduction methods of finite spaces to prove a generalization of Thomason's theorem on homotopy colimits over posets. In particular, this allows us to characterize the homotopy colimits of diagrams of simplicial complexes in terms of the Grothendieck construction on the diagrams of their face posets. We also derive analogues of well known results on homotopy colimits in the combinatorial setting, including a cofinality theorem and a generalization of Quillen's Theorem A for posets.
publishDate 2016
dc.date.none.fl_str_mv 2016-01
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/11336/55511
Fernández, Ximena Laura; Minian, Elias Gabriel; Homotopy colimits of diagrams over posets and variations on a theorem of Thomason; International Press Boston; Homology, Homotopy And Applications (hha); 18; 2; 1-2016; 233-245
1532-0073
CONICET Digital
CONICET
url http://hdl.handle.net/11336/55511
identifier_str_mv Fernández, Ximena Laura; Minian, Elias Gabriel; Homotopy colimits of diagrams over posets and variations on a theorem of Thomason; International Press Boston; Homology, Homotopy And Applications (hha); 18; 2; 1-2016; 233-245
1532-0073
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://arxiv.org/abs/1407.5646
info:eu-repo/semantics/altIdentifier/doi/10.4310/HHA.2016.v18.n2.a13
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
dc.publisher.none.fl_str_mv International Press Boston
publisher.none.fl_str_mv International Press Boston
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
_version_ 1842268931694264320
score 12.885934

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