Lemma 15.59.14. Let $R$ be a ring. Let $K^\bullet , L^\bullet $ be complexes of $R$-modules. There is a canonical isomorphism

functorial in both complexes which uses a sign of $(-1)^{pq}$ for the map $K^ p \otimes _ R L^ q \to L^ q \otimes _ R K^ p$ (see proof for explanation).

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