Thomason Model Structures in Every Strict Higher Dimension

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 ${\mathrm{Ex}}^2{N}_n$, and the Quillen equivalence is given by $c_n{\mathrm{Sd}}^2⊣{\mathrm{Ex}}^2{N}_n$. Thus strict higher categories model the homotopy theory of spaces in every positive finite dimension and in dimension ω.