Example 7.1.2.7. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category containing objects $X$ and $Y$. Then the unique morphism $e: \emptyset \rightarrow \operatorname{Hom}_{\operatorname{\mathcal{C}}}(X,Y)$ exhibits $X$ as a power of $Y$ by the empty simplicial set $\emptyset $ if and only if $X$ is a final object of $\operatorname{\mathcal{C}}$. Similarly, $e$ exhibits $Y$ as a copower of $X$ by $\emptyset $ set if and only if $Y$ is an initial object of $\operatorname{\mathcal{C}}$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$