= Primitive decomposition of an atomic finite-surjection sheaf
{title2=$F\cong\coprod_C F_C$}
Partition the elements of a sheaf by their primitive-ancestor equivalence classes under bijection. Each class gives a sheaf subfunctor, because its membership is preserved and reflected along covering surjections. A representative primitive element names an epic representable map onto its class component. Thus every sheaf is the coproduct of these components, each an <atom in a topos>.
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