Definition 1.1.0.11. Let $S_{\bullet }$ be a simplicial set and let $n$ be a nonnegative integer. An $n$-simplex of $S_{\bullet }$ is an element of the set $S_{n}$. We will also refer to elements of $S_{0}$ as vertices of $S_{\bullet }$, and to elements of $S_{1}$ as edges of $S_{\bullet }$. We often write $v \in S_{\bullet }$ to indicate that $v$ is a vertex of $S_{\bullet }$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$