Volume 20, issue 3 (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
Model structures for $(\infty,n)$–categories on (pre)stratified simplicial sets and prestratified simplicial spaces

Viktoriya Ozornova and Martina Rovelli

Algebraic & Geometric Topology 20 (2020) 1543–1600
Abstract

We prove the existence of a model structure on the category of stratified simplicial sets whose fibrant objects are precisely n–complicial sets, which are a proposed model for (,n)–categories, based on previous work of Verity and Riehl. We then construct a Quillen equivalent model based on simplicial presheaves over a category that can facilitate the comparison with other established models.

Keywords
stratified simplicial sets, complicial sets, $(\infty,n)$–categories, model categories
Mathematical Subject Classification 2010
Primary: 18D05, 55U10, 55U35
References
Publication
Received: 11 January 2019
Revised: 10 July 2019
Accepted: 26 August 2019
Published: 27 May 2020
Authors
Viktoriya Ozornova
Fakultät für Mathematik
Ruhr-University Bochum
Bochum
Germany
Martina Rovelli
Department of Mathematics
Johns Hopkins University
Baltimore, MD
United States
Mathematical Sciences Institute
The Australian National University
Canberra, ACT
Australia