Let $Y,Z$ be sets. We define a functor $F:Set\rightarrow Set$ in the following manner:
$F(X)=Hom(X,Y)\amalg Hom(X,Z)$, $F(f)=Hom(X,f)\amalg Hom(X,f)$.
How to prove that $F$ is not representable unless one of $Y,Z$ is empty?
Thank you in anticipation.