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.

## Comments (0)