Lemma 13.19.7. Let \mathcal{A} be an abelian category. Consider a solid diagram
\xymatrix{ K^\bullet & L^\bullet \ar[l]^\alpha \\ P^\bullet \ar[u] \ar@{-->}[ru]_{\beta _ i} }
where P^\bullet is bounded above and consists of projective objects, and \alpha is a quasi-isomorphism. Any two morphisms \beta _1, \beta _2 making the diagram commute up to homotopy are homotopic.
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