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...

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Authors: Caviglia, Giovanni, Gutiérrez Marín, Javier J.
Format: article
Status:Published version
Publication Date:2019
Country:España
Institution:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repository:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2445/194384
Online Access:https://hdl.handle.net/2445/194384
Access Level:Open access
Keyword:Teoria de l'homotopia
Categories (Matemàtica)
Homotopy theory
Categories (Mathematics)
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spelling 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 Gruyter2023202320192023info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersion24 p.application/pdfhttps://hdl.handle.net/2445/194384Articles publicats en revistes (Matemàtiques i Informàtica)reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)InglésReproducció 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:recercat.cat:2445/1943842026-05-29T05:05:01Z
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
2023
2023
2023
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
rights_invalid_str_mv (c) Walter de Gruyter, 2019
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 24 p.
application/pdf
dc.publisher.none.fl_str_mv Walter de Gruyter
publisher.none.fl_str_mv Walter de Gruyter
dc.source.none.fl_str_mv Articles publicats en revistes (Matemàtiques i Informàtica)
reponame:Recercat. Dipósit de la Recerca de Catalunya
instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
instname_str Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
reponame_str Recercat. Dipósit de la Recerca de Catalunya
collection Recercat. Dipósit de la Recerca de Catalunya
repository.name.fl_str_mv
repository.mail.fl_str_mv
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