Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$

Remark 1.1.3.3. Let $f: S_{\bullet } \rightarrow T_{\bullet }$ be a map of simplicial sets. If $\sigma$ is a degenerate $n$-simplex of $S_{\bullet }$, then $f(\sigma )$ is a degenerate $n$-simplex of $T_{\bullet }$. The converse holds if $f$ is a monomorphism of simplicial sets (for example, if $S_{\bullet }$ is a simplicial subset of $T_{\bullet }$).