Exercise 6.1.6.12. Let $k$ be a field and let $\operatorname{Vect}_{k}$ denote the category of vector spaces over $k$, equipped with the monoidal structure described in Example 2.1.3.1. Show that an object $V \in \operatorname{Vect}_{k}$ is left (or right) dualizable if and only if it is finite-dimensional as a vector space over $k$.
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