Thomason model structures in all strict higher dimensions
OpenAI research collection · 1 manuscript · Source checked 2026-10-19
OpenAI's result summary
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.
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MANUSCRIPT 01
Thomason Model Structures in Every Strict Higher Dimension
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…
Full source abstract
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 Ex^2N_n, and the Quillen equivalence is given by c_nSd^2\dashvEx^2N_n. Thus strict higher categories model the homotopy theory of spaces in every positive finite dimension and in dimension ω.
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