# Commutativity of a sheaf of groups from an epimorphism

Let $F$ and $G$ be sheaves of groups $\mathcal{S}^{op}\to Groups$ and $f:F\to G$ an epimorphism (of sheaves of sets).

If $F$ is a sheaf of commutative groups, is $G$ also a sheaf of commutative groups?

If $f$ would be a surjection on every section then for $x,y\in G(V)$ there would be $x', y'\in F(V)$ with $f(V)(x')=x$ and $f(V)(y')=y$ and $$xy=f(V)(x')f(V)(y')=f(V)(x'y')=f(V)(y'x')=f(V)(y')f(V)(x')=yx.$$ but $f$ is only surjective on stalks.

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