functor

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English[edit]

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Noun[edit]

functor (plural functors)

  1. (grammar) a function word
  2. (computing) a function object
  3. (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:XY of C is mapped to a morphism F(f): F(X) → F(Y) of D, such that if  h = g \circ f then  F(h) = F(g) \circ F(f), 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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