Bainbridge, Freyd, Scedrov and Scott have introduced functorial polymorphism to formalize parametricity in polymorphism. Here, the author goes on in more depth; he gives a generalization of the notion of a functor, developing a theory of ``structors''. Structors are used to define a parametric polymorphism such that intrinsic definitions of the basic data types are allowed. The results of the paper show that functors are particular structors, and dinatural transformations between bifunctors are transformations between structors. Related to polymorphism, the variable types are interpreted as structors, and terms as transformation between structors.