Lemma 29.15.5 (01T5)—The Stacks project

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Part 2: Schemes
Chapter 29: Morphisms of Schemes
Section 29.15: Morphisms of finite type
Lemma 29.15.5 (cite)

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Lemma 29.15.5. A closed immersion is of finite type. An immersion is locally of finite type.

Proof. This is true because an open immersion is a local isomorphism, and a closed immersion is obviously of finite type. $\square$

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