{"id":"openai-math/Thomason-Model-Structures-in-Every-Strict-Higher-Dimension","pdf":"https://github.com/openai/math/blob/main/preprints/Thomason-Model-Structures-in-Every-Strict-Higher-Dimension-September-25-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Thomason-Model-Structures-in-Every-Strict-Higher-Dimension-September-25-2026","tags":["higher-category-theory","model-categories","homotopy-theory"],"score":0,"title":"Thomason Model Structures in Every Strict Higher Dimension","domain":"Topology","family":"317","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.GT","summary":"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 .","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-25","reactions":{},"formalized":false,"family_title":"Thomason model structures in all strict higher dimensions"}