Lemma 90.27.7. Let \mathcal{F} be category cofibered in groupoids over \mathcal{C}_\Lambda . Assume there exist presentations of \mathcal{F} by minimal smooth prorepresentable groupoids in functors (U, R, s, t, c) and (U', R', s', t', c'). Then (U, R, s, t, c) and (U', R', s', t', c') are isomorphic.
Proof. Follows from Lemma 90.27.5 and the observation that a morphism [U/R] \to [U'/R'] is the same thing as a morphism of groupoids in functors (by our explicit construction of [U/R] in Definition 90.21.9). \square
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