This is a quite useful and commonly applied criterion, because one does not have to explicitly construct the "inverse" "G" and the natural isomorphisms between "FG", "GF" and the identity functors. On the other hand, though the above properties guarantee the "existence" of a categorical equivalence (given a sufficiently strong version of the axiom of choice in the underlying set theory), the missing data is not completely specified, and often there are many choices. It is a good idea to specify the missing constructions explicitly whenever possible.