Lemma 22.28.3. Let $R$ be a ring. Let $(A, \text{d})$ and $(B, \text{d})$ be differential graded algebras over $R$. The construction above defines an equivalence of categories

$\begin{matrix} \text{differential graded} \\ (A, B)\text{-bimodules} \end{matrix} \longleftrightarrow \begin{matrix} \text{right differential graded } \\ A^{opp} \otimes _ R B\text{-modules} \end{matrix}$

Proof. Immediate from discussion the above. $\square$

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