The problem is to show that the functor from the category of small categories to the category of sets that sends a category to its set of morphisms is representable.
The major problem is to find a small category $S$ such that for any small category $A$, the set $Cat(S,A)$ is bijective to $Mor(A)$. Isn't there only one distinguished category, namely $1$? But $1$ doesn't work.