Lemma 42.33.4. Let $(S, \delta )$ be as in Situation 42.7.1. Let $f : X \to Y$ and $g : Y \to Z$ be morphisms of schemes locally of finite type over $S$. Let $c \in A^ p(X \to Z)$ and assume $f$ is proper. Then the rule that to $Z' \to Z$ assigns $\alpha \longmapsto f'_*(c \cap \alpha )$ is a bivariant class denoted $f_* \circ c \in A^ p(Y \to Z)$.

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