Lemma 100.6.3 (04YD)—The Stacks project

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Table of contents
Part 7: Algebraic Stacks
Chapter 100: Properties of Algebraic Stacks
Section 100.6: Quasi-compact algebraic stacks
Lemma 100.6.3 (cite)

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Lemma 100.6.3. A finite disjoint union of quasi-compact algebraic stacks is a quasi-compact algebraic stack.

Proof. This is clear from the corresponding topological fact. $\square$

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