The Stacks project

Lemma 87.24.2. Let $S$ be a scheme. Let $f : X \to Y$ be a morphism of formal algebraic spaces over $S$. The following are equivalent

  1. $f$ is of finite type,

  2. $f$ is representable by algebraic spaces and is of finite type in the sense of Bootstrap, Definition 80.4.1.

Proof. This follows from Bootstrap, Lemma 80.4.5, the implication “quasi-compact $+$ locally of finite type $\Rightarrow $ finite type” for morphisms of algebraic spaces, and Lemma 87.17.5. $\square$

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