Remark 2.5.5.8. By taking Construction 2.5.5.7 as our definition of the chain complex $\mathrm{N}_{\ast }(A)$, we have adopted the perspective that $\mathrm{N}_{\ast }(A)$ is a quotient of the Moore complex $\mathrm{C}_{\ast }(A)$. However, it can also be realized as a subcomplex of the Moore complex $\mathrm{C}_{\ast }(A)$: see Construction 2.5.6.15 and Proposition 2.5.6.17.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$