Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Example 9.1.4.3. Recall that a functor of $\infty $-categories $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ is essentially surjective if, for every object $D \in \operatorname{\mathcal{D}}$, there exists an object $C \in \operatorname{\mathcal{C}}$ and an isomorphism $v: D \xrightarrow {\sim } F(C)$ (Definition 4.8.1.1). It follows that every essentially surjective functor is weakly right cofinal.