## FUNCTOR

### Functor

In mathematics, a functor is a type of mapping between categories, which is applied in category theory. Functors can be thought of as homomorphisms between categories. In the category of small categories, functors can be thought of more generally as morphisms.

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### functor

#### Noun

1. a function word
2. a function object
3. 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:XY of C is mapped to a morphism F(f): F(X) → F(Y) of D, such that if [itex] h = g \circ f [/itex] then [itex] F(h) = F(g) \circ F(f)[/itex], and such that identity morphisms (and only identity morphisms) are mapped to identity morphisms. Note: the functor just described is covariant.

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