# functor

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## functor

[′fəŋk·tər] (computer science)

(mathematics)

A function between categories which associates objects with objects and morphisms with morphisms.

## 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.

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.

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