Kerodon

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

Corollary 2.5.6.14. The normalized chain complex functor

\[ \mathrm{N}_{\ast }( -; \operatorname{\mathbf{Z}}): \operatorname{Set_{\Delta }}\rightarrow \operatorname{Ch}(\operatorname{\mathbf{Z}}) \]

admits a right adjoint, given on objects by the functor $M_{\ast } \mapsto \mathrm{K}( M_{\ast } )$ of Construction 2.5.6.3.