论文标题
$ \ infty $ -operads的Arity近似
Arity Approximation of $\infty$-Operads
论文作者
论文摘要
令$ \ mathbb {e} _d $用$ 1 \ le d \ le \ infty $表示小碟片，让$ \ mathcal {c} $为$ \ infty $ - 类别的所有映射空间均为$ n $ n $。我们证明，在考虑$ \ mathbb {e} _d $ -monoids中的$ \ mathcal {c} $时，所有相干图$> n+3 $都是多余的。更一般而言，对于$ \ infty $ -OPERAD $ \ MATHCAL {O} $，我们就与$ \ Mathcal {O} $相关的某些操作分区复合物的连接限制了相关连贯图的差异。
Let $\mathbb{E}_d$ denote the little discs operad for $1 \le d \le \infty$ and let $\mathcal{C}$ be an $\infty$-category all of whose mapping spaces are $n$-truncated. We prove that when considering $\mathbb{E}_d$-monoids in $\mathcal{C}$, all coherence diagrams of arity $>n+3$ are redundant. More generally, for an $\infty$-operad $\mathcal{O}$ we bound the arity of the relevant coherence diagrams in terms of the connectivity of certain operadic partition complexes associated to $\mathcal{O}$.
