Remark 1.2.5.5. Let $S$ be a simplicial set. Combining Example 1.2.5.4 with Proposition 1.2.1.13, we deduce that $S_{\bullet }$ is a Kan complex if and only if each connected component of $S$ is a Kan complex.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$