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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