Remark 8.3.3.6 (Duality). Let $\operatorname{\mathcal{C}}$ be an $\infty $-category, let $\mathscr {H}: \operatorname{\mathcal{C}}^{\operatorname{op}} \times \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{S}}$ be a functor, and let $\mathscr {H}': \operatorname{\mathcal{C}}\times \operatorname{\mathcal{C}}^{\operatorname{op}} \rightarrow \operatorname{\mathcal{S}}$ be the functor obtained from $\mathscr {H}$ by transposing its arguments. If $\mathscr {H}$ is a $\operatorname{Hom}$-functor for $\operatorname{\mathcal{C}}$, then $\mathscr {H}'$ is a $\operatorname{Hom}$-functor for the opposite $\infty $-category $\operatorname{\mathcal{C}}^{\operatorname{op}}$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$