Translator Disclaimer
2019 The universality of the Rezk nerve
Aaron Mazel-Gee
Algebr. Geom. Topol. 19(7): 3217-3260 (2019). DOI: 10.2140/agt.2019.19.3217

Abstract

We functorially associate to each relative –category ( , W ) a simplicial space N R ( , 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 N R ( , W ) is precisely the one corresponding to the localization [ [ W 1 ] ] ; and (ii) that the Rezk nerve functor defines an equivalence el C at [ [ W BK 1 ] ] C at from a localization of the –category of relative –categories to the –category of –categories.

Citation

Download Citation

Aaron Mazel-Gee. "The universality of the Rezk nerve." Algebr. Geom. Topol. 19 (7) 3217 - 3260, 2019. https://doi.org/10.2140/agt.2019.19.3217

Information

Received: 8 December 2015; Revised: 13 January 2019; Accepted: 29 January 2019; Published: 2019
First available in Project Euclid: 3 January 2020

zbMATH: 07162206
MathSciNet: MR4045352
Digital Object Identifier: 10.2140/agt.2019.19.3217

Subjects:
Primary: 18A05, 55U35

Rights: Copyright © 2019 Mathematical Sciences Publishers

JOURNAL ARTICLE
44 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.19 • No. 7 • 2019
MSP
Back to Top