Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 317-01. Thomason Model Structures in Every Strict Higher Dimension
Manuscript map · lines 8575–8584
OpenAI@2026-10-07#rem:oai-p-317-01
Authors: OpenAI. Family 317.
Title: Thomason Model Structures in Every Strict Higher Dimension.
Abstract: 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.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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