Lemma 63.6.4 (0F5C)—The Stacks project

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Part 3: Topics in Scheme Theory
Chapter 63: More Étale Cohomology
Section 63.6: Upper shriek for locally quasi-finite morphisms
Lemma 63.6.4 (cite)

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Lemma 63.6.4. Let $j : U \to X$ and $j' : V \to U$ be étale morphisms. The isomorphism $(j \circ j')^{-1} = (j')^{-1} \circ j^{-1}$ and the isomorphism $(j \circ j')^! = (j')^! \circ j^!$ of Lemma 63.6.3 agree via the isomorphism of Lemma 63.6.2.

Proof. Omitted. $\square$

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