The Stacks project

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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