Thomason model structures in all strict higher dimensions

What OpenAI claims

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)

Paper

1. Thomason Model Structures in Every Strict Higher Dimension

   25 September 2026 · Preprint, not peer reviewed · PDF

   We prove the higher-dimensional Thomason model-structure conjecture of Ara and Maltsiniotis. For every 1 ≤ n ≤ ∞, 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 Ex²N_n, and the Quillen equivalence is given by c_nSd²⊣Ex²N_n. Thus strict higher categories model the homotopy theory of spaces in every positive finite dimension and in dimension ω.

Status

Preprint. The paper has not been independently reviewed. Treat the result as OpenAI's claim until other mathematicians have checked it. If a video exists, it illustrates the statement; it is not the proof.