Example 1.2.5.6. Let $S$ be a discrete simplicial set (Definition 1.1.5.10). Then every connected component of $S$ is isomorphic to the standard simplex $\Delta ^{0}$, which is a Kan complex. Applying Remark 1.2.5.5, we see that $S$ is a Kan complex.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$