Tiny covariant representable functor on a category with binary coproducts

For a small category $\mathcal{C}$ with binary coproducts, exponentiation by $h_A=\mathcal{C}(A,-)$ in $[\mathcal{C},\mathbf{Set}]$ is naturally $F\mapsto F(-⨿A)$: the exponential at $B$ is $\mathrm{Nat}(h_B\times h_A,F)\cong \mathrm{Nat}(h_{B⨿A},F)\cong F(B⨿A)$ by the Yoneda lemma. This precomposition functor has a right adjoint given by Right Kan extension, so $h_A$ is a tiny object.