nLab coevaluation map

If $(\mathcal{C}, \otimes)$ is a monoidal category and $X \in \mathcal{C}$ a dualizable object with dual object $X^\ast$, the structure morphism

$$\mathbb{I} \to X \otimes X^\ast$$

is also called the coevaluation map, in contrast to the other structure map

$$X^\ast \otimes X \to \mathbb{I}$$

which is the evaluation map.