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functor (plural functors)

  1. (grammar) A function word.
  2. (object-oriented programming) A function object.
  3. (category theory) A category homomorphism; a morphism from a source category to a target category which maps objects to objects and arrows to arrows, in such a way as to preserve domains and codomains (of the arrows) as well as composition and identities.
    In the category of categories,  , the objects are categories and the morphisms are functors.
    • 1991, Natalie Wadhwa (translator), Yu. A. Brudnyǐ, N. Ya. Krugljak, Interpolation Functors and Interpolation Spaces, Volume I, Elsevier (North-Holland), page 143,
      Choosing for   the operation of closure, regularization or relative completion, we obtain from a given functor   the functors
    • 2004, William G. Dwyer, Philip S. Hirschhorn, Daniel M. Kan, Jeffrey H. Smith, Homotopy Limit Functors on Model Categories and Homotopical Categories, American Mathematical Society, page 165,
      Given a homotopical category   and a functor  , a homotopical  -colimit (resp.  -limit) functor on   will be a homotopically terminal (resp. initial) Kan extension of the identity (50.2) along the induced diagram functor   (47.1).
    • 2009, Benoit Fresse, Modules Over Operads and Functors, Springer, Lecture Notes in Mathematics: 1967, page 35,
      In this chapter, we recall the definition of the category of  -objects and we review the relationship between  -objects and functors. In short, a  -object (in English words, a symmetric sequence of objects, or simply a symmetric object) is the coefficient sequence of a generalized symmetric functor  , defined by a formula of the form


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functor m (plural functores)

  1. (category theory) functor (a mapping between categories)