2011/11/30 by Barwick, Clark, Schommer-Pries, Christopher · 1 citation
#Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics
paper · doi:10.48550/arxiv.1112.0040
We axiomatise the theory of (∞,n)-categories. We prove that the space of theories of (∞,n)-categories is a B(ℤ/2)n. We prove that Rezk's complete Segal Θn-spaces, Simpson and Tamsamani's Segal n-categories, the first author's n-fold complete Segal spaces, Kan and the first author's n-relative categories, and complete Segal space objects in any model of (∞,n-1)-categories all satisfy our axioms. Consequently, these theories are all equivalent in a manner that is unique up to the action of (ℤ/2)n.