# Kerodon

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Definition 8.2.1.3. Let $\lambda = (\lambda _{-}, \lambda _{+}): \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{C}}_{-}^{\operatorname{op}} \times \operatorname{\mathcal{C}}_{+}$ be a coupling of $\infty$-categories.

• We say that $\lambda$ is representable if, for every object $C_{+} \in \operatorname{\mathcal{C}}_{+}$, there exists a universal object $C \in \operatorname{\mathcal{C}}$ satisfying $\lambda _{+}(C) = C_{+}$.

• We say that $\lambda$ is corepresentable if, for every object $C_{-} \in \operatorname{\mathcal{C}}_{-}$, there exists a couniversal object $C \in \operatorname{\mathcal{C}}$ satisfying $\lambda _{-}(C) = C_{-}$.