Example 2.5.5.10. Let $S_{\bullet } = \Delta ^0$ be the standard $0$-simplex. Then the normalized chain complex $\mathrm{N}_{\ast }(S; \operatorname{\mathbf{Z}})$ can be identified with abelian group $\operatorname{\mathbf{Z}}$, regarded as a chain complex concentrated in degree zero. Note that the calculation of Example 2.5.5.4 shows that the quotient map $\mathrm{C}_{\ast }(S; \operatorname{\mathbf{Z}}) \twoheadrightarrow \mathrm{N}_{\ast }(S; \operatorname{\mathbf{Z}})$ induces an isomorphism on homology.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$