Definition 99.11.8. Let $\mathcal{X}$ be an algebraic stack. Let $x \in |\mathcal{X}|$.

We say the

*residual gerbe of $\mathcal{X}$ at $x$ exists*if the equivalent conditions (1), (2), and (3) of Lemma 99.11.7 hold.If the residual gerbe of $\mathcal{X}$ at $x$ exists, then the

*residual gerbe of $\mathcal{X}$ at $x$*^{1}is the strictly full subcategory $\mathcal{Z}_ x \subset \mathcal{X}$ constructed in Lemma 99.11.7.

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Comment #964 by Niels Borne on

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