Lemma 106.6.7. The category $p : \mathcal{C} \to W_{spaces, {\acute{e}tale}}$ constructed in Remark 106.6.1 is a gerbe.
Proof. In Lemma 106.6.4 we have seen that it is a stack in groupoids. Thus it remains to check conditions (2) and (3) of Stacks, Definition 8.11.1. Condition (2) follows from Lemma 106.6.5. Condition (3) follows from Lemma 106.6.6. $\square$
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