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2019-02-07

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/194384

Morita homotopy theory for $(\infty, 1)$-categories and $\infty$-operads

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https://doi.org/10.1515/forum-2018-0033

Abstract

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.

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Teoria de l'homotopia, Categories (Matemàtica)

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Homotopy theory, Categories (Mathematics)

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Articles publicats en revistes (Matemàtiques i Informàtica)

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CAVIGLIA, Giovanni and GUTIÉRREZ MARÍN, Javier J. Morita homotopy theory for $(\infty, 1)$-categories and $\infty$-operads. Forum Mathematicum. 2019. Vol. 31, num. 3, pags. 661-684. ISSN 0933-7741. [consulted: 11 of June of 2026]. Available at: https://hdl.handle.net/2445/194384

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