Adjoint functors requiring a natural bijection When showing that two functors $F:A\rightarrow B$ and $G:B\rightarrow A$ are adjoint, one defines a natural bijection $\mathrm{Mor}(X,G(Y)) \rightarrow \mathrm{Mor}(F(X),Y)$. What if one do not require the bijection to be natural, what issues would arise? 

Consider this example: take $A$ and $B$ to both be the category of non-zero finite dimensional real vector spaces; then all $\mathrm{Mor}(U,V)$ have the same cardinality, making any two endofunctors adjoint in the unnatural sense!
