Morita homotopy theory for $(\infty, 1)$-categories and $\infty$-operads
We prove the existence of Morita model structures on the categories of small simplicial categories, simplicial sets, simplicial operads and dendroidal sets, modelling the Morita homotopy theory of $(\infty, 1)$-categories and $\infty$-operads. We give a characterization of the weak equivalences in t...
| Autores: | , |
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| Tipo de documento: | artigo |
| Estado: | Versão publicada |
| Data de publicação: | 2019 |
| País: | España |
| Recursos: | Universidad de Barcelona |
| Repositório: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:diposit.ub.edu:2445/194384 |
| Acesso em linha: | https://hdl.handle.net/2445/194384 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Teoria de l'homotopia Categories (Matemàtica) Homotopy theory Categories (Mathematics) |
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Morita homotopy theory for $(\infty, 1)$-categories and $\infty$-operadsCaviglia, GiovanniGutiérrez Marín, Javier J.Teoria de l'homotopiaCategories (Matemàtica)Homotopy theoryCategories (Mathematics)We prove the existence of Morita model structures on the categories of small simplicial categories, simplicial sets, simplicial operads and dendroidal sets, modelling the Morita homotopy theory of $(\infty, 1)$-categories and $\infty$-operads. We give a characterization of the weak equivalences in terms of simplicial presheaves, simplicial algebras and slice categories. In the case of the Morita model structure for simplicial categories and simplicial operads, we also show that each of these model structures can be obtained as an explicit left Bousfield localization of the Bergner model structure on simplicial categories and the Cisinski-Moerdijk model structure on simplicial operads, respectively.Walter de Gruyter2019info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://hdl.handle.net/2445/194384Articles publicats en revistes (Matemàtiques i Informàtica)reponame:Dipòsit Digital de la UBinstname:Universidad de BarcelonaInglésReproducció del document publicat a: https://doi.org/10.1515/forum-2018-0033Forum Mathematicum, 2019, vol. 31, num. 3, p. 661-684https://doi.org/10.1515/forum-2018-0033(c) Walter de Gruyter, 2019info:eu-repo/semantics/openAccessoai:diposit.ub.edu:2445/1943842026-05-27T06:46:51Z |
| dc.title.none.fl_str_mv |
Morita homotopy theory for $(\infty, 1)$-categories and $\infty$-operads |
| title |
Morita homotopy theory for $(\infty, 1)$-categories and $\infty$-operads |
| spellingShingle |
Morita homotopy theory for $(\infty, 1)$-categories and $\infty$-operads Caviglia, Giovanni Teoria de l'homotopia Categories (Matemàtica) Homotopy theory Categories (Mathematics) |
| title_short |
Morita homotopy theory for $(\infty, 1)$-categories and $\infty$-operads |
| title_full |
Morita homotopy theory for $(\infty, 1)$-categories and $\infty$-operads |
| title_fullStr |
Morita homotopy theory for $(\infty, 1)$-categories and $\infty$-operads |
| title_full_unstemmed |
Morita homotopy theory for $(\infty, 1)$-categories and $\infty$-operads |
| title_sort |
Morita homotopy theory for $(\infty, 1)$-categories and $\infty$-operads |
| dc.creator.none.fl_str_mv |
Caviglia, Giovanni Gutiérrez Marín, Javier J. |
| author |
Caviglia, Giovanni |
| author_facet |
Caviglia, Giovanni Gutiérrez Marín, Javier J. |
| author_role |
author |
| author2 |
Gutiérrez Marín, Javier J. |
| author2_role |
author |
| dc.subject.none.fl_str_mv |
Teoria de l'homotopia Categories (Matemàtica) Homotopy theory Categories (Mathematics) |
| topic |
Teoria de l'homotopia Categories (Matemàtica) Homotopy theory Categories (Mathematics) |
| description |
We prove the existence of Morita model structures on the categories of small simplicial categories, simplicial sets, simplicial operads and dendroidal sets, modelling the Morita homotopy theory of $(\infty, 1)$-categories and $\infty$-operads. We give a characterization of the weak equivalences in terms of simplicial presheaves, simplicial algebras and slice categories. In the case of the Morita model structure for simplicial categories and simplicial operads, we also show that each of these model structures can be obtained as an explicit left Bousfield localization of the Bergner model structure on simplicial categories and the Cisinski-Moerdijk model structure on simplicial operads, respectively. |
| publishDate |
2019 |
| dc.date.none.fl_str_mv |
2019 |
| 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 |
https://hdl.handle.net/2445/194384 |
| url |
https://hdl.handle.net/2445/194384 |
| dc.language.none.fl_str_mv |
Inglés |
| language_invalid_str_mv |
Inglés |
| dc.relation.none.fl_str_mv |
Reproducció del document publicat a: https://doi.org/10.1515/forum-2018-0033 Forum Mathematicum, 2019, vol. 31, num. 3, p. 661-684 https://doi.org/10.1515/forum-2018-0033 |
| dc.rights.none.fl_str_mv |
(c) Walter de Gruyter, 2019 info:eu-repo/semantics/openAccess |
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(c) Walter de Gruyter, 2019 |
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openAccess |
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application/pdf |
| dc.publisher.none.fl_str_mv |
Walter de Gruyter |
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Walter de Gruyter |
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Articles publicats en revistes (Matemàtiques i Informàtica) reponame:Dipòsit Digital de la UB instname:Universidad de Barcelona |
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Universidad de Barcelona |
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Dipòsit Digital de la UB |
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Dipòsit Digital de la UB |
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15,300719 |