The Stacks project

Definition 106.3.3. We say an algebraic stack $\mathcal{X}'$ is a first order thickening of an algebraic stack $\mathcal{X}$ if $\mathcal{X}$ is a closed substack of $\mathcal{X}'$ and $\mathcal{X} \to \mathcal{X}'$ is a first order thickening in the sense of Properties of Stacks, Section 100.3.