Volume 19, issue 7 (2019)

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

Volume 23
Issue 6, 2415–2924
Issue 5, 1935–2414
Issue 4, 1463–1934
Issue 3, 963–1462
Issue 2, 509–962
Issue 1, 1–508

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

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
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
Other MSP Journals
This article is available for purchase or by subscription. See below.
The universality of the Rezk nerve

Aaron Mazel-Gee

Algebraic & Geometric Topology 19 (2019) 3217–3260

We functorially associate to each relative –category (,W) a simplicial space NR(,W), called its Rezk nerve (a straightforward generalization of Rezk’s “classification diagram” construction for relative categories). We prove the following local and global universal properties of this construction: (i) that the complete Segal space generated by the Rezk nerve NR(,W) is precisely the one corresponding to the localization [[W1]]; and (ii) that the Rezk nerve functor defines an equivalence elCat[[WBK1]] Cat from a localization of the –category of relative –categories to the –category of –categories.

PDF Access Denied

We have not been able to recognize your IP address as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

$\infty$–category, relative $\infty$–category, localization, Rezk nerve, classification diagram
Mathematical Subject Classification 2010
Primary: 18A05, 55U35
Received: 8 December 2015
Revised: 13 January 2019
Accepted: 29 January 2019
Published: 17 December 2019
Aaron Mazel-Gee
Department of Mathematics
University of Southern California
Los Angeles, CA
United States