Functor

:For functors in computer science, see the function object article.

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In category theory, a functor is a special type of mapping between categories. Functors can be thought of as morphisms in the category of small categories.

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Functors were first considered in algebraic topology, where algebraic objects (like the fundamental group) are associated to topological spaces, and algebraic homomorphisms are associated to continuous maps. Nowadays, functors are used throughout modern mathematics to relate various categories.

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Computer science: Computer science (abbreviated CS or compsci) encompasses a variety of topics that relates to computation, like abstract analysis of algorithms, formal grammars, and subjects such as programming languages, program design, software, computer hardware, artificial intelligence, and numerical analysis. B...

Function object: A function object, often called a functor, is a computer programming construct allowing an object to be invoked or called as if it were an ordinary function, usually with the same syntax. The exact meaning may vary among programming languages. A functor used in this manner in computing bears littl...

Category theory: Category theory is a mathematical theory that deals in an abstract way with mathematical structures and relationships between them. It is half-jokingly known as "generalized abstract nonsense". Categories appear in most branches of mathematics, in some areas of theoretical computer science and mathe...