每个严格高维中的Thomason模型结构
Thomason Model Structures in Every Strict Higher Dimension
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具体内容
该稿件研究Ara与Maltsiniotis提出的高维Thomason模型结构猜想。作者声称，对每个1≤n≤∞，小严格球状n-范畴的范畴具有一个真组合模型结构，且Quillen等价于单纯集；弱等价与纤维化由二次扩张的Street神经Ex²Nₙ检测，Quillen等价由cₙSd²⊣Ex²Nₙ给出。若成立，则严格高范畴在每一正有限维及ω维中建模空间的同伦论。
- 声称证明Ara–Maltsiniotis高维Thomason模型结构猜想
- 弱等价与纤维化由二次扩张Street神经Ex²Nₙ检测
- Quillen等价由cₙSd²⊣Ex²Nₙ给出，覆盖1≤n≤∞
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英文原始摘要
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.
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