= Slice of a set-valued functor category
{title2=$[\mathcal C,\mathbf{Set}]/F\simeq[\int F,\mathbf{Set}]$}
A <natural transformation> $P\to F$ assigns a set of points over every element $x\in F(c)$. These fibers form a <functor> on the <category of elements> of $F$. Conversely, a functor on the category of elements gives $P(c)$ as the disjoint union of its values over all $x\in F(c)$. The two constructions are inverse up to natural isomorphism. Smallness of $\mathcal C$ makes the category of elements small and allows this description to transfer Cartesian closure to every slice.
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