# Kerodon

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

Corollary 2.5.7.15. Let $S_{\bullet }$ and $T_{\bullet }$ be simplicial sets. Then the Eilenberg-Zilber homomorphism

$\mathrm{EZ}: \mathrm{N}_{\ast }(S; \operatorname{\mathbf{Z}}) \boxtimes \mathrm{N}_{\ast }(T; \operatorname{\mathbf{Z}}) \rightarrow \mathrm{N}_{\ast }(S \times T; \operatorname{\mathbf{Z}})$

is a quasi-isomorphism.