Volume 20, issue 6 (2020)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 20
Issue 7, 3219–3760
Issue 6, 2687–3218
Issue 5, 2145–2685
Issue 4, 1601–2143
Issue 3, 1073–1600
Issue 2, 531–1072
Issue 1, 1–529

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
A relative $2$–nerve

Fernando Abellán García, Tobias Dyckerhoff and Walker H Stern

Algebraic & Geometric Topology 20 (2020) 3147–3182
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.

Keywords
relative nerve, Grothendieck construction, bicategories
Mathematical Subject Classification 2010
Primary: 18D30, 18E35, 18G30, 18G55
References
Publication
Received: 18 October 2019
Revised: 13 January 2020
Accepted: 22 January 2020
Published: 8 December 2020
Authors
Fernando Abellán García
Fachbereich Mathematik
Universität Hamburg
Hamburg
Germany
Tobias Dyckerhoff
Fachbereich Mathematik
Universität Hamburg
Hamburg
Germany
Walker H Stern
Department of Mathematics
University of Virginia
Charlottesville, VA
United States