Pronunciation Noun

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.
    hypo en
    In the category of categories, \mathbb{CAT}, 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 U the operation of closure, regularization or relative completion, we obtain from a given functor \mathcal{F}\in\mathcal{JF} the functors
      \overline{F} : \overrightarrow{X} \rightarrow \overline{F(\overrightarrow{X})}, F^0 : \overrightarrow{X}\rightarrow F(\overrightarrow{X})^0, F^c : \overrightarrow{X} \rightarrow F(\overrightarrow{X})^c.
    • 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 X and a functor u: A \rightarrow B, a homotopical u-colimit (resp. u-limit) functor on X will be a homotopically terminal (resp. initial) Kan extension of the identity (50.2) along the induced diagram functor X^u: X^B \rightarrow X^A (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 \Sigma_*-objects and we review the relationship between \Sigma_*-objects and functors. In short, a \Sigma_*-object (in English words, a symmetric sequence of objects, or simply a symmetric object) is the coefficient sequence of a generalized symmetric functor S(M) : X\rightarrow S(M,X), defined by a formula of the form
      S(M,X) = \bigoplus^\infty_{r=0} \left ( M(r)\otimes X^{\otimes r}\right )_{\Sigma_r}.
Translations Translations
  • French: foncteur
  • German: Funktor
  • Italian: funtore
  • Portuguese: functor, funtor
  • Russian: функтор
  • Spanish: funtor

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