Functor meaning

fŭngk'tər
One that performs an operation or a function.
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(grammar) A function word.
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(computing) A function object.
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(category theory) A structure-preserving mapping between categories: if F is a functor from category C to category D, then F maps objects of C to objects of D and morphisms of C to morphisms of D such that any morphism f:X→Y of C is mapped to a morphism F(f): F(X) → F(Y) of D, such that if then , and such that identity morphisms (only identity morphisms) are mapped to identity morphisms. Note: the functor just described is covariant.
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Origin of functor

New Latin fūnctor from Latin fūnctiō performance, function function