Let $A$ and $B$ be objects of the category $C$ and assume $I$ and $H$ are covariant functors from $C$ into $\text{Sets}$ such that $I(X) = \operatorname{mor}(B,X)$ and $H(X) = \operatorname{mor}(A,X)$ and $I(f)(g) = f\circ g$ and $H(f)(g) = f\circ g$. Then if $D: I \rightarrow H$ is a natural transformation then there exists a morphism $d:A \to B$ such that $D_X (g) = g\circ d$ for every $X$ in $C$.
I have tried to use the definition of natural transformation coupled with morphisms $f: A \to X$ or $f:B \to X$ in order to get to the required morphism but it does not lead me anywhere. Any hints would be appreciated.Thanks.