Lemma 22.7.5. Let $(A, \text{d})$ be a differential graded algebra. Let $L_1 \to L_2 \to \ldots \to L_ n$ be a sequence of composable homomorphisms of differential graded $A$-modules. There exists a commutative diagram
in $\text{Mod}_{(A, \text{d})}$ such that each $M_ i \to M_{i + 1}$ is an admissible monomorphism and each $M_ i \to L_ i$ is a homotopy equivalence.
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