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Functor - Wikipedia

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In mathematics, specifically category theory, a functor is a mapping between categories. Functors were first considered in algebraic topology, where algebraic objects (such as the fundamental group) are associated to topological spaces, and maps between these algebraic objects are associated to continuous maps between spaces. Nowadays, functors are used throughout modern mathematics to relate various categories. Thus, functors are important in all areas within mathematics to which category theory is applied. The words category and functor were borrowed by mathematicians from the philosophers Aristotle and Rudolf Carnap, respectively.[1] The latter used functor in a linguistic context;[2] see function word. Let C and D be categories. A functor F from C to D is a mapping that[3] That is, functors must preserve identity morphisms and composition of morphisms. There are many constructions in mathematics that would be functors but for the fact that they "turn morphisms around" and "reverse

Functor - Wikipedia Jump to content From Wikipedia, the free encyclopedia Mapping between categories This article is about the mathematical concept. For other uses, see Functor (disambiguation) . "Functoriality" redirects here. For the Langlands functoriality conjecture in number theory, see Langlands program § Functoriality . In mathematics , specifically category theory , a functor is a mapping between categories . Functors were first considered in algebraic topology , where algebraic objects (such as the fundamental group ) are associated to topological spaces , and maps between these algeb

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