Solution
= Solution
Suppose $F:\mathbf{Set}\to\mathcal C$ is a <left adjoint> to $U$. The <adjunction> gives <bijections>, natural in $X$,
$$
\mathcal C(F1,X)\cong\mathbf{Set}(1,U X)\cong U X.
$$
The second map is evaluation at the singleton element, as in part (a). Thus \b[$U$ is represented by $F1$]. This argument uses the one-point set as a generator of the particular set-valued adjunction; it does not claim that every arbitrary right adjoint is representable.