http://en.wikipedia.org/wiki/Natural_transformation

If F and G are functors between the categories C and D, then a natural transformation η from F to G associates to every object X in C a morphism ηX : F(X) → G(X) in D called the component of η at X, such that for every morphism f : X → Y in C we have ηY o F(f) = G(f) o ηX.

If, for every object X in C, the morphism ηX is an isomorphism in D, then η is said to be a natural isomorphism (or sometimes natural equivalence or isomorphism of functors). Two functors F and G are called naturally isomorphic or simply isomorphic if there exists a natural isomorphism from F to G.

Так что, у меня изначально было правильно или нет?
Запутался окончательно.