Exercise 111.30.13. Let $\mathcal{A}$ be an abelian category. Consider a solid diagram

of complexes of $\text{Fil}^ f(\mathcal{A})$. Assume $K^\bullet $, $L^\bullet $ and $I^\bullet $ bounded below and each $I^ n$ a filtered injective object. Also assume $\alpha $ a filtered quasi-isomorphism. Any two morphisms $\beta _1, \beta _2$ making the diagram commute up to homotopy are homotopic.

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