Lemma 76.42.3 (08B5)—The Stacks project

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Table of contents
Part 4: Algebraic Spaces
Chapter 76: More on Morphisms of Spaces
Section 76.42: Grothendieck's existence theorem
Lemma 76.42.3 (cite)

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Lemma 76.42.3. The functor (76.42.2.1) is exact.

Proof. It suffices to check this étale locally on $X$ , see Lemma 76.42.1. Thus we reduce to the case of schemes which is Cohomology of Schemes, Lemma 30.23.4. $\square$

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