Kerodon

Definition 6.1.6.8. Let $\operatorname{\mathcal{C}}$ be a monoidal category. We will say that a morphism $\operatorname{coev}: {\bf 1} \rightarrow Y \otimes X$ in $\operatorname{\mathcal{C}}$ is a duality datum if it satisfies the equivalent conditions of Variant 6.1.6.7: that is, if there exists a morphism $\operatorname{ev}: X \otimes Y \rightarrow {\bf 1}$ for which the pair $(\operatorname{coev}, \operatorname{ev})$ is a duality datum in the sense of Definition 6.1.6.1.