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What (who) is functor - definition

IN CATEGORY THEORY, A MAPPING BETWEEN CATEGORIES THAT PRESERVES THEIR STRUCTURE (IDENTITY MORPHISMS, COMPOSITION OF MORPHISMS)

Covariant functor; Contravariant functor; Cofunctor; Functorial; Functors; Functoriality; Endofunctor; Bifunctor; Covariance and contravariance of functors; Identity functor; Multifunctor; Functor (category theory); Covariance (categories); Opposite functor; Constant functor; Selection functor; Category homomorphism; Dual functor; Covariance and contravariance (category theory)

functor

In category theory, a functor F is an operator on types. F is also considered to be a polymorphic operator on functions with the type F : (a -> b) -> (F a -> F b). Functors are a generalisation of the function "map". The type operator in this case takes a type T and returns type "list of T". The map function takes a function and applies it to each element of a list. (1995-02-07)

functor

['f??kt?]

¦ noun Logic & Mathematics a function; an operator.

Functor

In mathematics, specifically category theory, a functor is a [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.

https://en.wikipedia.org/wiki/Functor

Wikipedia

Functor

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. The latter used functor in a linguistic context; see function word.

https://en.wikipedia.org/wiki/Functor