# Kerodon

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

Example 7.1.6.3. Let $U: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a functor of $\infty$-categories. The following conditions are equivalent:

• The functor $U$ is fully faithful.

• Every object of $\operatorname{\mathcal{C}}$ is $U$-initial.

• Every object of $\operatorname{\mathcal{C}}$ is $U$-final.