Lemma 22.28.5. Let R be a ring. Let (A, \text{d}) and (B, \text{d}) be differential graded R-algebras. Let P be a differential graded (A, B)-bimodule having property (P) with corresponding filtration F_\bullet , then we obtain a short exact sequence
0 \to \bigoplus \nolimits F_ iP \to \bigoplus \nolimits F_ iP \to P \to 0
of differential graded (A, B)-bimodules which is split as a sequence of graded (A, B)-bimodules.
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