Remark 1.1.2.6. Let $f: S_{\bullet } \rightarrow T_{\bullet }$ be a morphism of simplicial sets. If every nondegenerate simplex of $T_{\bullet }$ belongs to the image of $f$, then $f$ is an epimorphism: that is, it induces a surjection $S_{n} \twoheadrightarrow T_{n}$ for each $n \geq 0$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$