A functor maps objects and morphisms between categories while preserving identities and composition.
A covariant functor is representable when it is naturally isomorphic to for some object ; a contravariant functor is representable when it is naturally isomorphic to .
The Yoneda lemma gives natural bijections
(1)
and their contravariant analogues.
A functor is full and faithful when every map
(1)
is a bijection.

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Functor by Wikipedia Bot 1
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In the context of computer science, a **functor** is a design pattern that originates from category theory in mathematics. It is a type that can be mapped over, which means it implements a mapping function that applies a function to each element within its context. ### In Programming Languages 1.
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