Example 4.8.8.4. For $n \leq -2$, Theorem 4.8.8.3 asserts that every functor of $\infty $-categories $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ admits a factorization $\operatorname{\mathcal{C}}\xrightarrow {F'} \operatorname{\mathcal{D}}' \xrightarrow {G} \operatorname{\mathcal{D}}$, where the functor $G$ is an equivalence of $\infty $-categories. This is trivial: we can take $\operatorname{\mathcal{D}}' = \operatorname{\mathcal{D}}$ and $G$ to be the identity functor.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$