# Kerodon

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

Proposition 2.5.5.11. For every simplicial abelian group $A_{\bullet }$, the quotient map $\mathrm{C}_{\ast }(A) \twoheadrightarrow \mathrm{N}_{\ast }(A)$ is a quasi-isomorphism of chain complexes: that is, it induces an isomorphism on homology groups.