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
Famous quotes containing the word natural:
“What journeyings on foot and on horseback through the wilderness, to preach the gospel to these minks and muskrats! who first, no doubt, listened with their red ears out of a natural hospitality and courtesy, and afterward from curiosity or even interest, till at length there “were praying Indians,” and, as the General Court wrote to Cromwell, the “work is brought to this perfection that some of the Indians themselves can pray and prophesy in a comfortable manner.””
—Henry David Thoreau (1817–1862)