Lemma 15.58.3. Let $R$ be a ring. The homotopy category $K(R)$ of complexes of $R$-modules endowed with the functor $(L^\bullet , M^\bullet ) \mapsto \text{Tot}(L^\bullet \otimes _ R M^\bullet )$ and associativity and commutativity constraints as above is a symmetric monoidal category.

Proof. This follows from Lemmas 15.58.1 and 15.58.2. Details omitted. $\square$

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