Thomason model structures in all strict higher dimensions. Resolves the Ara–Maltsiniotis conjecture: for every n ≥ 1 and n = ω, small strict globular n-categories admit proper combinatorial Thomason model structures Quillen equivalent to simplicial sets. Thus strict higher categories model the homotopy theory of spaces in every stated dimension.
released 2026-09-25 | 3 theorems · 14 lemmas · 26 proofs · 16,941 words |
PLAY LEVEL 1 »(pdf)
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 ω.