Exercise 111.30.13. Let $\mathcal{A}$ be an abelian category. Consider a solid diagram
\[ \xymatrix{ K^\bullet \ar[r]_\alpha \ar[d]_\gamma & L^\bullet \ar@{-->}[dl]^{\beta _ i} \\ I^\bullet } \]
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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