The Stacks project

Lemma 62.6.2. Let $\alpha $ be a relative $r$-cycle on $X/S$ as in Definition 62.6.1. Then any restriction, base change, flat pullback, or proper pushforward of $\alpha $ is a relative $r$-cycle.

Proof. For flat pullback use Lemma 62.4.4. Restriction is a special case of flat pullback. To see it holds for base change use that base change is transitive. For proper pushforward use Lemma 62.4.5. $\square$

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