Lemma 105.6.7. The category $p : \mathcal{C} \to W_{spaces, {\acute{e}tale}}$ constructed in Remark 105.6.1 is a gerbe.

Proof. In Lemma 105.6.4 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 105.6.5. Condition (3) follows from Lemma 105.6.6. $\square$

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