Remark 7.1.5.7. Let $U: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a functor of $\infty $-categories and let $Y \in \operatorname{\mathcal{C}}$ be an object. Suppose that $U(Y)$ is a final object of $\operatorname{\mathcal{D}}$. Then $Y$ is a final object of $\operatorname{\mathcal{C}}$ if and only if it is a $U$-final object of $\operatorname{\mathcal{C}}$ (apply Remark 7.1.5.6 in the special case $\operatorname{\mathcal{E}}= \Delta ^0$).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$