Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Remark 1.1.9.6. Let $S_{\bullet }$ be a simplicial set. Combining Example 1.1.9.5 with Proposition 1.1.6.13, we deduce that $S_{\bullet }$ is a Kan complex if and only if each connected component of $S_{\bullet }$ is a Kan complex.