Kerodon

Remark 8.3.2.19. Let $\lambda : \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{C}}_{-}^{\operatorname{op}} \times \operatorname{\mathcal{C}}_{+}$ be a coupling of $\infty $-categories and let $\mathscr {K}: \operatorname{\mathcal{C}}_{-}^{\operatorname{op}} \times \operatorname{\mathcal{C}}_{+} \rightarrow \operatorname{\mathcal{S}}$ be a covariant transport representation for $\lambda $. Then the coupling $\lambda $ is balanced (in the sense of Definition 8.2.6.1) if and only if the profunctor $\mathscr {K}$ is balanced (in the sense of Definition 8.3.2.18). See Remark 8.3.2.8.