Lemma 20.4.2. Let $X$ be a topological space. Let $\mathcal{G}$ be a sheaf of (possibly non-commutative) groups on $X$. A $\mathcal{G}$-torsor $\mathcal{F}$ is trivial if and only if $\mathcal{F}(X) \not= \emptyset $.

**Proof.**
Omitted.
$\square$

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