Lemma 114.8.26. Let $f : X \to Y$ and $g : Y \to Z$ be composable locally quasi-finite morphisms of schemes. Then $g_! \circ f_! = (g \circ f)_!$ and $f^! \circ g^! = (g \circ f)^!$.

Proof. Combination of More Étale Cohomology, Lemmas 62.4.12 and 62.6.3. $\square$

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