A functor $F$ defines a subfunctor of $G$ if there is a natural transformation $\alpha \colon F \Rightarrow G$ whose components are monomorphisms. In the case of $G \colon \mathsf{C}^\mathrm{op} \to \textup{\textsf{cat}}$, a subfunctor is given by a collection of subsets $Fc \subset Gc$ so that each $Gf \colon Gc \to Gc’$ restricts to a function $Ff \colon Fc \to Fc’$. Characterize those subsets that assemble into a subfunctor of the representable functor $\mathsf{C}(-,c)$.