Lemma 21.5.2. Let $\mathcal{C}$ be a site. Let $\mathcal{G}$ be a sheaf of (possibly non-commutative) groups on $\mathcal{C}$. A $\mathcal{G}$-torsor $\mathcal{F}$ is trivial if and only if $\Gamma (\mathcal{C}, \mathcal{F}) \not= \emptyset $.

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

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