Lemma 106.3.5 (0BPS)—The Stacks project

Table of contents
Part 7: Algebraic Stacks
Chapter 106: More on Morphisms of Stacks
Section 106.3: Thickenings
Lemma 106.3.5 (cite)

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Lemma 106.3.5. If $\mathcal{X} \subset \mathcal{X}'$ and $\mathcal{X}' \subset \mathcal{X}''$ are thickenings of algebraic stacks, then so is $\mathcal{X} \subset \mathcal{X}''$.

Proof. See discussion above, Properties of Stacks, Section 100.3, and More on Morphisms of Spaces, Lemma 76.9.9 $\square$

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