Example 3.5.6.8. Let $X$ be a Kan complex, let $\pi _0(X)$ be the set of connected components of $X$. Then the fundamental $0$-groupoid $\pi _{\leq 0}(X)$ can be identified with the constant simplicial set $\underline{ \pi _0(X) }$. More precisely, the tautological map $X \rightarrow \underline{ \pi _0(X) }$ exhibits $\underline{\pi _0(X) }$ as a fundamental $0$-groupoid of $X$ (see Proposition 3.5.5.7).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$