- category theory in nLab
Category term was initially introduced to define a Functor. So the whole Category Theory is better described as a theory of Functors. (That’s not a valid definition, but reflect the present and historical motivation.)
(But Functors are too complex to be suitable as the basis of the theory.)
Furthermore, the term Functor was first defined with the purpose of defining a natural transformation. So Category Theory is about natural transformations.