functor

  1. Noun.  (grammar) a function word.
  2. Noun.  (computing) a function object.
  3. Noun.  (mathematics) 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 arrows of ''C'' to arrows of ''D'' such that any arrow ''f'':''X''→''Y'' of ''C'' is mapped to an arrow ''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 arrows (and only identity arrows) are mapped to identity arrows. Note: the functor just described is covariant.

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This entry was last updated on RefTopia from its source on 3/20/2012.