Homotopy theory of non-symmetric operads, II: Change of base category and left properness
We prove, under mild assumptions, that a Quillen equivalence between symmetric monoidal model categories gives rise to a Quillen equivalence between their model categories of (non-symmetric) operads, and also between model categories of algebras over operads. We also show left properness results on...
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2014 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/43024 |
| Acceso en línea: | http://hdl.handle.net/11441/43024 https://doi.org/10.2140/agt.2014.14.229 |
| Access Level: | acceso abierto |
| Palabra clave: | operad algebra model category Quillen equivalence A–infinity algebra |
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Homotopy theory of non-symmetric operads, II: Change of base category and left propernessMuro Jiménez, Fernandooperadalgebramodel categoryQuillen equivalenceA–infinity algebraWe prove, under mild assumptions, that a Quillen equivalence between symmetric monoidal model categories gives rise to a Quillen equivalence between their model categories of (non-symmetric) operads, and also between model categories of algebras over operads. We also show left properness results on model categories of operads and algebras over operads. As an application, we prove homotopy invariance for (unital) associative operads.Junta de AndalucíaMinisterio de Educación y CienciaFondo Europeo de Desarrollo RegionalGeneralitat de CatalunyaMathematical Sciences PublishersÁlgebraFQM218: Geometria Algebraica, Sistemas Diferenciales y Singularidades2014info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/11441/43024https://doi.org/10.2140/agt.2014.14.229reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésAlgebraic and Geometric Topology, 14, 229-281.FQM-5713MTM2010-15831SGR-119-2009info:eu-repo/semantics/openAccessoai:idus.us.es:11441/430242026-06-17T12:51:07Z |
| dc.title.none.fl_str_mv |
Homotopy theory of non-symmetric operads, II: Change of base category and left properness |
| title |
Homotopy theory of non-symmetric operads, II: Change of base category and left properness |
| spellingShingle |
Homotopy theory of non-symmetric operads, II: Change of base category and left properness Muro Jiménez, Fernando operad algebra model category Quillen equivalence A–infinity algebra |
| title_short |
Homotopy theory of non-symmetric operads, II: Change of base category and left properness |
| title_full |
Homotopy theory of non-symmetric operads, II: Change of base category and left properness |
| title_fullStr |
Homotopy theory of non-symmetric operads, II: Change of base category and left properness |
| title_full_unstemmed |
Homotopy theory of non-symmetric operads, II: Change of base category and left properness |
| title_sort |
Homotopy theory of non-symmetric operads, II: Change of base category and left properness |
| dc.creator.none.fl_str_mv |
Muro Jiménez, Fernando |
| author |
Muro Jiménez, Fernando |
| author_facet |
Muro Jiménez, Fernando |
| author_role |
author |
| dc.contributor.none.fl_str_mv |
Álgebra FQM218: Geometria Algebraica, Sistemas Diferenciales y Singularidades |
| dc.subject.none.fl_str_mv |
operad algebra model category Quillen equivalence A–infinity algebra |
| topic |
operad algebra model category Quillen equivalence A–infinity algebra |
| description |
We prove, under mild assumptions, that a Quillen equivalence between symmetric monoidal model categories gives rise to a Quillen equivalence between their model categories of (non-symmetric) operads, and also between model categories of algebras over operads. We also show left properness results on model categories of operads and algebras over operads. As an application, we prove homotopy invariance for (unital) associative operads. |
| publishDate |
2014 |
| dc.date.none.fl_str_mv |
2014 |
| dc.type.none.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion |
| format |
article |
| status_str |
publishedVersion |
| dc.identifier.none.fl_str_mv |
http://hdl.handle.net/11441/43024 https://doi.org/10.2140/agt.2014.14.229 |
| url |
http://hdl.handle.net/11441/43024 https://doi.org/10.2140/agt.2014.14.229 |
| dc.language.none.fl_str_mv |
Inglés |
| language_invalid_str_mv |
Inglés |
| dc.relation.none.fl_str_mv |
Algebraic and Geometric Topology, 14, 229-281. FQM-5713 MTM2010-15831 SGR-119-2009 |
| dc.rights.none.fl_str_mv |
info:eu-repo/semantics/openAccess |
| eu_rights_str_mv |
openAccess |
| dc.format.none.fl_str_mv |
application/pdf application/pdf |
| dc.publisher.none.fl_str_mv |
Mathematical Sciences Publishers |
| publisher.none.fl_str_mv |
Mathematical Sciences Publishers |
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reponame:idUS. Depósito de Investigación de la Universidad de Sevilla instname:Universidad de Sevilla (US) |
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Universidad de Sevilla (US) |
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idUS. Depósito de Investigación de la Universidad de Sevilla |
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idUS. Depósito de Investigación de la Universidad de Sevilla |
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1869422371641753600 |
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15.301629 |