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

Ozornova, Viktoriya¹ ; Rovelli, Martina²

¹Fakultät für Mathematik, Ruhr-University Bochum, Bochum, Germany
²Department of Mathematics, Johns Hopkins University, Baltimore, MD, United States, Mathematical Sciences Institute, The Australian National University, Canberra, ACT, Australia

Algebraic and Geometric Topology, Tome 20 (2020) no. 3, pp. 1543-1600

Résumé

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.

Détail

DOI : 10.2140/agt.2020.20.1543

Classification : 18D05, 55U10, 55U35
Keywords: stratified simplicial sets, complicial sets, $(\infty,n)$–categories, model categories

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