Lemma 101.23.3 (06UB)—The Stacks project

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Part 7: Algebraic Stacks
Chapter 101: Morphisms of Algebraic Stacks
Section 101.23: Locally quasi-finite morphisms
Lemma 101.23.3 (cite)

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Lemma 101.23.3. A base change of a locally quasi-finite morphism is locally quasi-finite.

Proof. We have seen this for quasi-DM morphisms in Lemma 101.4.4 and for locally finite type morphisms in Lemma 101.17.3. It is immediate that the condition on fibres is inherited by a base change. $\square$

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