Example 1.1.2.4 (Degenerate Edges). Let $S_{\bullet }$ be a simplicial set and let $e$ be an edge of $S_{\bullet }$. Then $e$ is degenerate if and only if it has the form $\operatorname{id}_{x}$, for some vertex $x \in S_{\bullet }$. If this condition is satisfied, then the vertex $x$ is uniquely determined (since it is both the source and target of the edge $e$).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$