Remark 4.8.2.12. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ and $G: \operatorname{\mathcal{D}}\rightarrow \operatorname{\mathcal{E}}$ be functors of $\infty $-categories, where $F$ exhibits $\operatorname{\mathcal{D}}$ as a local $n$-truncation of $\operatorname{\mathcal{C}}$. Then $(G \circ F): \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{E}}$ exhibits $\operatorname{\mathcal{E}}$ as an $n$-truncation of $\operatorname{\mathcal{C}}$ if and only if $G$ is an equivalence of $\infty $-categories.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$