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
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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