OpenAI · 317-01 · 2026-09-25 · Topology
Thomason Model Structures in Every Strict Higher Dimension
preprints/Thomason-Model-Structures-in-Every-Strict-Higher-Dimension-September-25-2026
Family 317. Thomason model structures in every strict higher dimension.
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N
Resolves the Ara–Maltsiniotis conjecture: for every and , small strict globular -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.
We prove the higher-dimensional Thomason model-structure conjecture of Ara and Maltsiniotis. For every , 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 , and the Quillen equivalence is given by . Thus strict higher categories model the homotopy theory of spaces in every positive finite dimension and in dimension ω.
Preprint source and Lean scope
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This preprint is named in the Lean scope note for 317: Thomason model structures in all strict higher dimensions. The authors are OpenAI. This companion does not verify the formalization. It is not a premise. The OAI library is not imported. No compilation is asserted. O.1 stays NOT_CLOSED.