Lemma 13.19.4 (0647)—The Stacks project

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Table of contents
Part 1: Preliminaries
Chapter 13: Derived Categories
Section 13.19: Projective resolutions
Lemma 13.19.4 (cite)

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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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