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}
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