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2020 A relative $2$–nerve
Fernando Abellán García, Tobias Dyckerhoff, Walker H Stern
Algebr. Geom. Topol. 20(6): 3147-3182 (2020). DOI: 10.2140/agt.2020.20.3147

Abstract

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 –categorical localizations, corresponds to Lurie’s scaled unstraightening equivalence. In this –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. "A relative $2$–nerve." Algebr. Geom. Topol. 20 (6) 3147 - 3182, 2020. https://doi.org/10.2140/agt.2020.20.3147

Information

Received: 18 October 2019; Revised: 13 January 2020; Accepted: 22 January 2020; Published: 2020
First available in Project Euclid: 16 December 2020

MathSciNet: MR4185938
Digital Object Identifier: 10.2140/agt.2020.20.3147

Subjects:
Primary: 18D30, 18E35, 18G30, 18G55

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.20 • No. 6 • 2020
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