The Stacks project

Definition 87.24.1. Let $S$ be a scheme. Let $f : Y \to X$ be a morphism of formal algebraic spaces over $S$.

  1. We say $f$ is locally of finite type if $f$ is representable by algebraic spaces and is locally of finite type in the sense of Bootstrap, Definition 80.4.1.

  2. We say $f$ is of finite type if $f$ is locally of finite type and quasi-compact (Definition 87.17.4).

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