# Kerodon

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Variant 2.5.7.17. Let $S_{\bullet }$ and $T_{\bullet }$ be simplicial sets containing simplicial subsets $S'_{\bullet }$ and $T'_{\bullet }$, respectively. Applying Theorem 2.5.7.14 to the simplicial abelian groups $\operatorname{\mathbf{Z}}[ S_{\bullet } ] / \operatorname{\mathbf{Z}}[ S'_{\bullet } ]$ and $\operatorname{\mathbf{Z}}[ T_{\bullet } ] / \operatorname{\mathbf{Z}}[ T'_{\bullet } ]$, we obtain a quasi-isomorphism

$\mathrm{EZ}: \mathrm{N}_{\ast }(S, S'; \operatorname{\mathbf{Z}}) \boxtimes \mathrm{N}_{\ast }(T, T'; \operatorname{\mathbf{Z}}) \rightarrow \mathrm{N}_{\ast }(S \times T, (S' \times T) \cup (S \times T'); \operatorname{\mathbf{Z}}),$