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 category theory and consequently appear in the majority of its applications.

Read more about Natural Transformation: Definition, Unnatural Isomorphism, Operations With Natural Transformations, Functor Categories, Yoneda Lemma, Historical Notes, Symbols Used

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### Famous quotes containing the word natural:

“The *natural* historian is not a fisherman who prays for cloudy days and good luck merely; but as fishing has been styled “a contemplative man’s recreation,” introducing him profitably to woods and water, so the fruit of the naturalist’s observations is not in new genera or species, but in new contemplations still, and science is only a more contemplative man’s recreation.”

—Henry David Thoreau (1817–1862)