Definition 3.5.5.1. Let $n$ be a nonnegative integer. An $n$-groupoid is a Kan complex $X$ which satisfies the following condition: for every pair of integers $0 \leq i \leq m$ with $m > n$, the restriction map $\operatorname{Hom}_{\operatorname{Set_{\Delta }}}( \Delta ^ m, X) \rightarrow \operatorname{Hom}_{\operatorname{Set_{\Delta }}}( \Lambda ^{m}_{i}, X )$ is a bijection.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$