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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

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.

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