Remark 1.2.1.20 ($\pi _0$ as a Colimit). Let $S_{}$ be a simplicial set. It follows from Proposition 1.2.1.19 that the component map $u: S_{} \rightarrow \underline{ \pi _0( S_{})}_{}$ exhibits $\pi _0( S_{} )$ as the colimit of the diagram $\operatorname{{\bf \Delta }}^{\operatorname{op}} \rightarrow \operatorname{Set}$ determined by $S_{}$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$