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

$a \cdot _{opp} b = (-1)^{\deg (a)\deg (b)} b a$

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

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