The Stacks project

Remark 22.29.2. Let $R$ be a ring. Let $(A, \text{d})$ and $(B, \text{d})$ be differential graded algebras over $R$. Let $N$ be a differential graded $(A, B)$-bimodule. Let $M$ be a right differential graded $A$-module. Then for every $k \in \mathbf{Z}$ there is an isomorphism

\[ (M \otimes _ A N)[k] \longrightarrow M[k] \otimes _ A N \]

of right differential graded $B$-modules defined without the intervention of signs, see More on Algebra, Section 15.72.

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