The Stacks project

Lemma 4.43.8. Let $\mathcal{C}$ be a monoidal category. If $Y_ i$, $i = 1, 2$ are left duals of $X_ i$, $i = 1, 2$, then $Y_2 \otimes Y_1$ is a left dual of $X_1 \otimes X_2$.

Proof. Follows from uniqueness of adjoints and Remark 4.43.7. $\square$

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