Lemma 43.7.2. Let $f : X \to Y$ and $g : Y \to Z$ be flat morphisms of varieties. Then $g \circ f$ is flat and $f^* \circ g^* = (g \circ f)^*$ as maps $Z_ k(Z) \to Z_{k + \dim (X) - \dim (Z)}(X)$.

**Proof.**
Special case of Chow Homology, Lemma 42.14.3.
$\square$

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