Lemma 100.45.7. Let $f : \mathcal{X} \to \mathcal{Y}$ be a morphism of algebraic stacks. Assume $f$ is étale, $f$ induces an isomorphism between automorphism groups at points (Remark 100.19.5), and for every algebraically closed field $k$ the functor

is an equivalence. Then $f$ is an isomorphism.

## Comments (2)

Comment #7856 by Rachel Webb on

Comment #8075 by Stacks Project on