Lemma 39.10.3. Situation as in Definition 39.10.2, The action $a$ is free if and only if
\[ G \times _ S X \to X \times _ S X, \quad (g, x) \mapsto (a(g, x), x) \]
is a monomorphism.
Lemma 39.10.3. Situation as in Definition 39.10.2, The action $a$ is free if and only if
is a monomorphism.
Proof. Immediate from the definitions. $\square$
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