The Stacks project

Lemma 42.63.5. Exterior product is associative. More precisely, let $(S, \delta )$ be as above, let $X, Y, Z$ be schemes locally of finite type over $S$, let $\alpha \in \mathop{\mathrm{CH}}\nolimits _*(X)$, $\beta \in \mathop{\mathrm{CH}}\nolimits _*(Y)$, $\gamma \in \mathop{\mathrm{CH}}\nolimits _*(Z)$. Then $(\alpha \times \beta ) \times \gamma = \alpha \times (\beta \times \gamma )$ in $\mathop{\mathrm{CH}}\nolimits _*(X \times _ S Y \times _ S Z)$.