# Kerodon

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

Remark 4.6.2.10. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a functor of $\infty$-categories, and let $\operatorname{\mathcal{D}}' \subseteq \operatorname{\mathcal{D}}$ be the essential image of $F$. Then $\operatorname{\mathcal{D}}'$ is a replete full subcategory of $\operatorname{\mathcal{D}}$, and $F$ can be regarded as an essentially surjective functor from $\operatorname{\mathcal{C}}$ to $\operatorname{\mathcal{D}}'$. Moreover, the essential image $\operatorname{\mathcal{D}}'$ is uniquely determined by these properties.