Model structures for (∞,n)–categories on (pre)stratified simplicial sets and prestratified simplicial spaces

Ozornova, Viktoriya; Rovelli, Martina

doi:10.2140/agt.2020.20.1543

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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

DOI: 10.2140/agt.2020.20.1543

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 $(\infty, n)$ –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

Volume 20, issue 3 (2020)