Kerodon

Example 4.8.8.5. When $n = -1$, 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 fully faithful and the functor $F'$ is essentially surjective. For example, we can take $\operatorname{\mathcal{D}}' \subseteq \operatorname{\mathcal{D}}$ to be the essential image of the functor $F$, and $G: \operatorname{\mathcal{D}}' \hookrightarrow \operatorname{\mathcal{D}}$ to be the inclusion map. See Remark 4.6.2.13.