Exercise 1.1.2.9. Let $S_{\bullet }$ be a simplicial set and let $\sigma $ be a $2$-simplex of $S_{\bullet }$. Show that $\sigma $ is both left-degenerate and right-degenerate if and only if it is constant: that is, it factors as a composition $\Delta ^2 \twoheadrightarrow \Delta ^0 \hookrightarrow S_{\bullet }$ (for a more general statement, see Proposition 1.1.3.8).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$