In
category theory, a branch of
mathematics, a
natural transformation provides a way of transforming one
functor into another while respecting the internal structure (i.e. the composition of
morphisms) of the
categories involved. Hence, a natural transformation can be considered to be a "morphism of functors". Indeed this intuition can be formalized to define so-called
functor categories. Natural transformations are, after categories and functors, one of the most fundamental notions of
category theory and consequently appear in the majority of its applications.