Kerodon

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

Definition 1.1.6.8 (Connected Components). Let $S_{\bullet }$ be a simplicial set. We will say that a simplicial subset $S'_{\bullet } \subseteq S_{\bullet }$ is a connected component of $S_{\bullet }$ if $S'_{\bullet }$ is a summand of $S_{\bullet }$ (Definition 1.1.6.1) and $S'_{\bullet }$ is connected (Definition 1.1.6.6). We let $\pi _0( S_{\bullet } )$ denote the set of all connected components of $S_{\bullet }$.