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 recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | Universidad de Barcelona |
| Repositorio: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:diposit.ub.edu:2445/194384 |
| Acceso en línea: | https://hdl.handle.net/2445/194384 |
| Access Level: | acceso abierto |
| Palabra clave: | Teoria de l'homotopia Categories (Matemàtica) Homotopy theory Categories (Mathematics) |
| Sumario: | 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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