ABSTRACT
In analyzing relationships between categories, functors play an obvious role. An isomorphism of categories, as A an example, is a functor that identifies exactly identical categories. However, this is an unduly strong notion of the similarity of categories. An equivalence of categories, on the other hand, is provided by an equivalence functor that identifies for people the similarity of the properties of the arrows in categories it connects. An adjunct situation between two categories shows people how a source of the first category is related to a source in the second category. When an adjoint situation occurs, the two involved categories possess an essentially identical structure for mathematical relationships for sources in them. The notion of a universal arrow is that of the relation of a source in one category with a source in the other category.
