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arXiv · 1910.06223

A relative 2-nerve

Fernando Abellán García·Tobias Dyckerhoff·Walker H. Stern
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Abstract

In this work, we introduce a 2-categorical variant of Lurie's relative nerve functor. We prove that it defines a right Quillen equivalence which, upon passage to $\infty$-categorical localizations, corresponds to Lurie's scaled unstraightening equivalence. In this $\infty$-bicategorical context, the relative 2-nerve provides a computationally tractable model for the Grothendieck construction which becomes equivalent, via an explicit comparison map, to Lurie's relative nerve when restricted to 1-categories.

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Fernando Abellán García, Tobias Dyckerhoff, Walker H. Stern. 2019-10-14. A relative 2-nerve. https://doi.org/10.2140/agt.2020.20.3147

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