The Stacks project

Lemma 78.8.3. Situation as in Definition 78.8.2, The action $a$ is free if and only if

\[ G \times _ B X \to X \times _ B X, \quad (g, x) \mapsto (a(g, x), x) \]

is a monomorphism of algebraic spaces.

Proof. Immediate from the definitions. $\square$

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