Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Remark 2.5.6.15. When regarded as a functor from $\operatorname{Ch}(\operatorname{\mathbf{Z}})$ to the category of simplicial sets, the functor $M_{\ast } \mapsto \mathrm{K}( M_{\ast } )$ fits into the paradigm of Variant 1.1.7.7: it is the functor $\operatorname{Sing}^{Q}_{\bullet }$ associated to the cosimplicial chain complex

\[ Q: \operatorname{{\bf \Delta }}\rightarrow \operatorname{Ch}(\operatorname{\mathbf{Z}}) \quad \quad [n] \mapsto \mathrm{N}_{\ast }( \Delta ^ n; \operatorname{\mathbf{Z}}). \]