Corollary 2.5.1.9. Let $f: C_{\ast } \rightarrow D_{\ast }$ be a chain map between chain complexes with values in an abelian category $\operatorname{\mathcal{A}}$. If $f$ is a chain homotopy equivalence, then it is a quasi-isomorphism.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$