The Stacks project

Definition 100.38.1. Let $f : \mathcal{X} \to \mathcal{Y}$ be a morphism of algebraic stacks. The scheme theoretic image of $f$ is the smallest closed substack $\mathcal{Z} \subset \mathcal{Y}$ through which $f$ factors1.

[1] We will see in Lemma 100.38.3 that the scheme theoretic image always exists.

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