Lemma 13.19.4. Let $\mathcal{A}$ be an abelian category. Let $K^\bullet $ be an acyclic complex. Let $P^\bullet $ be bounded above and consisting of projective objects. Any morphism $P^\bullet \to K^\bullet $ is homotopic to zero.

**Proof.**
Dual to Lemma 13.18.4.
$\square$

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