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. (Lean)
Manuscript
Thomason Model Structures in Every Strict Higher Dimension
September 25, 2026 · source · cite as \cite{OAI:Thomason-Model-Structures-in-Every-Strict-Higher-Dimension-September-25-2026}
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.
Result 317 · Topology. Imported from openai/math, a collection of manuscripts produced by an OpenAI model; results are at different stages of verification. Discussion below is by Lemma members.
Source: https://github.com/openai/math/blob/main/CONTENTS.md