Covariant Model Structures and Simplicial Localization
| Autor: | Stevenson, Danny |
|---|---|
| Rok vydání: | 2015 |
| Předmět: | |
| Zdroj: | North-West. Eur. J. Math. Vol. 3 (2017) pp. 141-202 |
| Druh dokumentu: | Working Paper |
| Popis: | In this paper we prove that for any simplicial set $B$, there is a Quillen equivalence between the covariant model structure on $\mathbf{S}/B$ and a certain localization of the projective model structure on the category of simplicial presheaves on the simplex category $\Delta/B$ of $B$. We extend this result to give a new Quillen equivalence between this covariant model structure and the projective model structure on the category of simplicial presheaves on the simplicial category $\mathfrak{C}[B]$. We study the relationship with Lurie's straightening theorem. Along the way we prove some results on localizations of simplicial categories and quasi-categories. Comment: v3: corrected some errors, final version, 49 pages |
| Databáze: | arXiv |
| Externí odkaz: |
|