In mathematics, specifically in category theory, the 2-category of small categories is the 2-category whose objects are small categories, whose arrows are functors and whose 2-arrows are natural transformations. Mathematics is the study of quantity, structure, space and change. ... Category theory is a mathematical theory that deals in an abstract way with mathematical structures and relationships between them. ... Category theory is a mathematical theory that deals in an abstract way with mathematical structures and relationships between them. ... In mathematics, categories allow one to formalize notions involving abstract structure and processes which preserve structure. ... In category theory, a functor is a special type of mapping between categories. ... In category theory, an abstract branch of mathematics, a natural transformation provides a way of transforming one functor into another while respecting the internal structure (i. ...
Categories appear in most branches of mathematics, in some areas of theoretical computer science and mathematical physics, and have been a unifying notion.
Categories were first introduced by Samuel Eilenberg and Saunders Mac Lane in 1945, in connection with algebraic topology.
Such a process is called a functor, and it associates to every object of one category an object of another category, and to every morphism in the first category a morphism in the second.
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