= Cokernel sheaf
{title2=$\operatorname{coker}\phi$}
For a <morphism of sheaves> $\phi:\mathcal F\to\mathcal G$ of abelian groups or modules, the cokernel sheaf is the <sheafification> of the <presheaf> $U\mapsto\mathcal G(U)/\phi(\mathcal F(U))$. Its <stalk> at $x$ is $\operatorname{coker}(\mathcal F_x\to\mathcal G_x)$. The presheaf quotient itself need not satisfy the <sheaf gluing axiom>, which explains why a surjective <morphism of sheaves> need not be surjective on <global sections>.
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