A relative 2-nerve
Algebraic Topology
2020-12-16 v3 Category Theory
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 -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.
Keywords
Cite
@article{arxiv.1910.06223,
title = {A relative 2-nerve},
author = {Fernando Abellán García and Tobias Dyckerhoff and Walker H. Stern},
journal= {arXiv preprint arXiv:1910.06223},
year = {2020}
}
Comments
30 pages, 1 figure, v2:minor revisions, v3: final version accepted for publication in Algebr. Geom. Topol