Definition 101.18.2 (06FY)—The Stacks project

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Table of contents
Part 7: Algebraic Stacks
Chapter 101: Morphisms of Algebraic Stacks
Section 101.18: Points of finite type
Definition 101.18.2 (cite)

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Definition 101.18.2. Let $\mathcal{X}$ be an algebraic stack. We say a point $x \in |\mathcal{X}|$ is a finite type point¹ if the equivalent conditions of Lemma 101.18.1 are satisfied. We denote $\mathcal{X}_{\text{ft-pts}}$ the set of finite type points of $\mathcal{X}$ .

[1] This is a slight abuse of language as it would perhaps be more correct to say “locally finite type point”.

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