A Quillen adjunction between globular and complicial approaches to (∞,n)-categories

2022/06/06 by Ozornova, Viktoriya, Rovelli, Martina
#18N50 #18N65 #55U10 #55U35 #Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2206.02689

Abstract

We prove the compatibility between the suspension construction and the complicial nerve of ω-categories. As a motivating application, we produce a Quillen pair between the models of (∞,n)-categories given by Rezk's complete Segal Θ_n-spaces and Verity's n-complicial sets.

Related

• Theory and models of (∞,ω)-categories
• The complicial model of (∞,ω)-categories
• An explicit comparison between 2-complicial sets and Θ₂-spaces
• Model ∞-categories II: Quillen adjunctions
• Modeling (∞,1)-categories with Segal spaces