Remark 5.4.2.7. In the situation of Lemma 5.4.2.6, we will see later that the converse assertion is also true: if $\sigma $ is a thin $2$-simplex of $\operatorname{\mathcal{C}}$, then $q(\sigma )$ is a thin $2$-simplex of $\operatorname{\mathcal{D}}$ (Proposition 5.4.7.10).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$