The Stacks project

Lemma 115.20.2. Notation and assumptions as above. The functor $\pi _!$ induces an equivalence of categories between

  1. the category $\textit{Lift}_\mathcal {O}(i_*\underline{\mathcal{G}}, A')$, and

  2. the category $\textit{Lift}(\mathcal{G}, A')$.

Proof. FIXME. $\square$

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