Kerodon

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

Definition 1.1.3.2. Let $S_{\bullet }$ be a simplicial set and let $\sigma : \Delta ^{n} \rightarrow S_{\bullet }$ be an $n$-simplex of $S_{\bullet }$. We will say that $\sigma $ is degenerate if $n > 0$ and $\sigma $ satisfies the equivalent conditions of Proposition 1.1.3.1. We say that $\sigma $ is nondegenerate if it is not degenerate (in particular, every $0$-simplex of $S_{\bullet }$ is nondegenerate).