Lemma 101.17.3 (06FU)—The Stacks project

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Part 7: Algebraic Stacks
Chapter 101: Morphisms of Algebraic Stacks
Section 101.17: Morphisms of finite type
Lemma 101.17.3 (cite)

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Lemma 101.17.3. A base change of a finite type morphism is finite type. The same holds for locally of finite type.

Proof. Combine Remark 101.16.4 with Morphisms of Spaces, Lemma 67.23.3. $\square$

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