Lemma 78.8.3 (06P9)—The Stacks project

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Table of contents
Part 4: Algebraic Spaces
Chapter 78: Groupoids in Algebraic Spaces
Section 78.8: Actions of group algebraic spaces
Lemma 78.8.3 (cite)

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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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