Editing Adjoint functors (section)

===Symmetry of optimization problems===

It is also possible to ''start'' with the functor ''F'', and pose the following (vague) question: is there a problem to which ''F'' is the most efficient solution?

The notion that ''F'' is the ''most efficient solution'' to the problem posed by ''G'' is, in a certain rigorous sense, equivalent to the notion that ''G'' poses the ''most difficult problem'' that ''F'' solves.

This gives the intuition behind the fact that adjoint functors occur in pairs: if ''F'' is left adjoint to ''G'', then ''G'' is right adjoint to ''F''.