Corollary 1.2.3.19. For every simplicial set $S$, we have a canonical bijection
\[ \pi _0(S ) \simeq \pi _0( | S | ). \]
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$
Corollary 1.2.3.19. For every simplicial set $S$, we have a canonical bijection
Proof. Writing $S$ as a disjoint union of connected components (Proposition 1.2.1.11, we can reduce to the case where $S$ is connected, in which case both sets have a single element (Proposition 1.2.3.18). $\square$