The Stacks project

Lemma 83.5.9. In the situation of Definition 83.5.8. A morphism $\phi : U \to X$ is set-theoretically $R$-invariant if and only if for any algebraically closed field $k$ over $B$ the map $U(k) \to X(k)$ is constant on orbits.

Proof. This is true because the condition is supposed to hold for all algebraically closed fields over $B$. $\square$

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