Definition 22.11.1. Let $R$ be a ring. Let $(A, \text{d})$ be a differential graded algebra over $R$. The *opposite differential graded algebra* is the differential graded algebra $(A^{opp}, \text{d})$ over $R$ where $A^{opp} = A$ as a graded $R$-module, $\text{d} = \text{d}$, and multiplication is given by

for homogeneous elements $a, b \in A$.

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