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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