The Ara-Maltsiniotis conjecture: Thomason model structures on strict n-categories for every n

Theorem 1.1: for every $n\in\{1,2,\dots\}\cup\{\infty\}$, the classes $W_n=N_n^{-1}(W_{KQ})$, $F_n=(\mathrm{Ex}^2N_n)^{-1}(\mathrm{Fib}_{KQ})$ and $C_n={}^{\perp}(F_n\cap W_n)$ form a proper combinatorial model structure on small strict $n$-categories, cofibrantly generated by the images of boundary and horn inclusions under $c_n\mathrm{Sd}^2$, and $c_n\mathrm{Sd}^2\dashv\mathrm{Ex}^2N_n$ is a Quillen equivalence with Kan-Quillen simplicial sets. The key step proves the Ara-Maltsiniotis pushout condition (Scholie 5.14 (d')). It concerns strict globular categories only, not weak higher categories or n-fold categories.

Theorem 1.1: for every $n\in\{1,2,\dots\}\cup\{\infty\}$, the classes $W_n=N_n^{-1}(W_{KQ})$, $F_n=(\mathrm{Ex}^2N_n)^{-1}(\mathrm{Fib}_{KQ})$ and $C_n={}^{\perp}(F_n\cap W_n)$ form a proper combinatorial model structure on small strict $n$-categories, cofibrantly generated by the images of boundary and horn inclusions under $c_n\mathrm{Sd}^2$, and $c_n\mathrm{Sd}^2\dashv\mathrm{Ex}^2N_n$ is a Quillen equivalence with Kan-Quillen simplicial sets. The key step proves the Ara-Maltsiniotis pushout condition (Scholie 5.14 (d')). It concerns strict globular categories only, not weak higher categories or n-fold categories.