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Covariant Model Structures and Simplicial Localization. (arXiv:1512.04815v3 [math.AT] UPDATED)

来源于:arXiv
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. 查看全文>>