AI 中文总结
研究行走余归纳等价的Roberts-Street神经得到的带标记单纯集，证明其为不可收缩的饱和复形集且有限截断均可收缩，给出右(∞,∞)-范畴不可收缩但到左(∞,∞)-范畴的反射可收缩的明确例子
AI 中文摘要
我们研究由行走余归纳等价的Roberts-Street nerve（神经）得到的带标记单纯集，证明它是一个不可收缩的饱和复形集，且其所有有限截断均为可收缩的。当将饱和复形集视为右$(\boldsymbol{\rightarrow}\boldsymbol{\rightarrow})$-范畴的模型时，它是一个具体明确的例子：该右$(\boldsymbol{\rightarrow}\boldsymbol{\rightarrow})$-范畴本身不可收缩，但它到左$(\boldsymbol{\rightarrow}\boldsymbol{\rightarrow})$-范畴的反射是可收缩的。
英文摘要
We study the marked simplicial set obtained as the Roberts-Street nerve of the walking coinductive equivalence. We show that it is a non-contractible saturated complicial set for which all of its finite truncations are contractible. When regarding saturated complicial sets as a model for right $(\infty,\infty)$-categories, it represents a concrete and explicit example of a right $(\infty,\infty)$-category that is itself non-contractible, but whose reflection to a left $(\infty,\infty)$-category is contractible.
