Thomason Model Structures in Every Strict Higher Dimension

Abstract — v2

We prove the higher-dimensional Thomason model-structure conjecture of Ara and Maltsiniotis. For every $1\le n\le\infty$, the category of small strict globular $n$-categories admits a proper combinatorial model structure that is Quillen equivalent to simplicial sets. Its weak equivalences and fibrations are detected by the twice-extended Street nerve $\mathrm{Ex}^2N_n$, and the Quillen equivalence is given by $c_n\mathrm{Sd}^2\dashv\mathrm{Ex}^2N_n$. Thus strict higher categories model the homotopy theory of spaces in every positive finite dimension and in dimension $\omega$.