Exercise 6.1.6.18. Let $\operatorname{\mathcal{C}}$ be a monoidal category containing objects $X$ and $Y$. Show that, if $X$ is weakly right dualizable and $Y$ is right dualizable, then the tensor product $X \otimes Y$ is weakly right dualizable (and that there is a canonical isomorphism $(X \otimes Y)^{\vee } \simeq Y^{\vee } \otimes X^{\vee }$).
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