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 basic notions of
categorical algebra and consequently appear in the majority of its applications.
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