Corollary 3.5.5.11. Let $n$ be a nonnegative integer and let $X$ be a Kan complex. If $X$ is $(n-1)$-coskeletal, then it is an $n$-groupoid. if $X$ is an $n$-groupoid, then it is $(n+1)$-coskeletal.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$
Corollary 3.5.5.11. Let $n$ be a nonnegative integer and let $X$ be a Kan complex. If $X$ is $(n-1)$-coskeletal, then it is an $n$-groupoid. if $X$ is an $n$-groupoid, then it is $(n+1)$-coskeletal.
Proof. Combine Proposition 3.5.5.10 with Remark 3.5.4.2. $\square$