# Functor meaning

One that performs an operation or a function.

noun

(grammar) A function word.

noun

(computing) A function object.

noun

(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*â†’*Y*of*C*is mapped to a morphism*F*(*f*):*F*(*X*) â†’*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.noun

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