Kerodon

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

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.