The Stacks project

Lemma 21.48.5. Let $(\mathcal{C}, \mathcal{O})$ be a ringed site. The derived category $D(\mathcal{O})$ is a symmetric monoidal category with tensor product given by derived tensor product with usual associativity and commutativity constraints (for sign rules, see More on Algebra, Section 15.72).

Proof. Omitted. Compare with Lemma 21.48.1. $\square$

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