Lemma 15.126.1. Let $R$ be a ring. The derived category $D(R)$ of $R$ is a symmetric monoidal category with tensor product given by derived tensor product and associativity and commutativity constraints as in Section 15.72.

**Proof.**
Omitted. Hints: The associativity constraint is the isomorphism of Lemma 15.59.15 and the commutativity constraint is the isomorphism of Lemma 15.59.14. Having said this the commutativity of various diagrams follows from the corresponding result for the category of complexes of $R$-modules, see Section 15.58.
$\square$

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