Let $\mathcal A$ be an abelian category, let $C = (C_n, d_C)$ and $D = (D_n, d_D)$ be chain complexes in $\mathcal A$, and let $f: C \to D$ be a chain map. Then $f$ is a quasi-isomorphism, meaning that $H_n(f): H_n(C) \to H_n(D)$ is an isomorphism for every $n \in \mathbb Z$, if and only if the mapping cone $\operatorname{Cone}(f)$ is acyclic, meaning that $H_n(\operatorname{Cone}(f)) = 0$ for every $n \in \mathbb Z$.