Notation 1.1.2.2. Let $S_{\bullet }$ be a simplicial set. Then the degeneracy operator $s^{0}_{0}: S_{0} \rightarrow S_{1}$ carries each vertex $x$ to an edge of $S_{\bullet }$ which we will denote by $\operatorname{id}_{x}$. Note that the vertex $x$ is both the source and target of the edge $\operatorname{id}_{x}$ (see Exercise 1.1.2.7).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$