Remark 8.2.3.2. Let $G,G': \operatorname{\mathcal{C}}_{+} \rightarrow \operatorname{\mathcal{C}}_{-}$ be functors which are isomorphic (as objects of the $\infty $-category $\operatorname{Fun}( \operatorname{\mathcal{C}}_{+}, \operatorname{\mathcal{C}}_{-} )$). Then a coupling $\lambda : \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{C}}_{-}^{\operatorname{op}} \times \operatorname{\mathcal{C}}_{+}$ is representable by $G$ if and only if it is representable by $G'$. See Proposition 5.1.7.5.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$