Remark 3.5.5.6. Let $\{ X_{j} \} _{j \in \operatorname{\mathcal{J}}}$ be a diagram of simplicial sets having limit $X = \varprojlim _{j \in \operatorname{\mathcal{J}}} X_ j$ and let $n$ be a nonnegative integer. If each $X_{j}$ is an $n$-groupoid and $X$ is a Kan complex, then $X$ is also an $n$-groupoid. In particular, any product of $n$-groupoids is an $n$-groupoid (see Example 1.2.5.3).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$