Remark 2.5.5.12. In the situation of Proposition 2.5.5.11, an even stronger statement holds: the quotient map $\mathrm{C}_{\ast }(A) \twoheadrightarrow \mathrm{N}_{\ast }(A)$ is a chain homotopy equivalence (Definition 2.5.0.5).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$