Sheaf morphism whose cokernel is not a sheaf

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Let $\mathcal{F}$ and $\mathcal{G}$ be sheafs of vector spaces. I am looking for an example of a sheaf morphism $\theta:\mathcal{F}\longrightarrow\mathcal{G}$ whose cokernel $\text{Coker}(\theta)$ is NOT a sheaf. There is this typical example with the exponential function which I have already studied, but I would like to have a different one. Does somebody have an idea?