Remark: Any characteristic class is a polynomial in Chern classes, for the reason as follows. Let formula_61 be the contravariant functor that, to a CW complex "X", assigns the set of isomorphism classes of complex vector bundles of rank "n" over "X" and, to a map, its pullback. By definition, a characteristic class is a natural transformation from formula_62 to the cohomology functor formula_63 Characteristic classes form a ring because of the ring structure of cohomology ring. Yoneda's lemma says this ring of characteristic classes is exactly the cohomology ring of "G""n":