Rigidification and the Coherent Nerve for Enriched Quasicategories

Harry Gindi

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arXiv · 1810.10075

Rigidification and the Coherent Nerve for Enriched Quasicategories

Harry Gindi

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Abstract

We introduce, for $\C$ a regular Cartesian Reedy category a model category whose fibrant objects are an analogue of quasicategories enriched in simplicial presheaves on $C$. We then develop a coherent realization and nerve for this model structure and demonstrate using an enriched version of the necklaces of Dugger and Spivak that our model category is Quillen-equivalent to the category of categories enriched in simplicial presheaves on $\C$. We then show that for any Cartesian-closed left-Bousfield localization of the category of simplicial presheaves on $\C$, the coherent nerve and realization descend to a Quillen equivalence on the localizations of these model categories. As an application, we demonstrate a version of Yoneda's lemma for these enriched quasicategories.

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Harry Gindi. 2018-10-23. Rigidification and the Coherent Nerve for Enriched Quasicategories. https://arxiv.org/abs/1810.10075

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