Definition 100.11.8. 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 100.11.7 hold.
If the residual gerbe of \mathcal{X} at x exists, then the residual gerbe of \mathcal{X} at x1 is the strictly full subcategory \mathcal{Z}_ x \subset \mathcal{X} constructed in Lemma 100.11.7.
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