Corollary 7.1.5.11. Let $U: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a functor of $\infty $-categories, and let $f: X \rightarrow Y$ be an isomorphism in $\operatorname{\mathcal{C}}$. Then the object $X$ is $U$-initial if and only if $Y$ is $U$-initial, and the object $X$ is $U$-final if and only if $Y$ is $U$-final.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$