Dictionary

functor en · NOUN

Pronunciation

• /ˈfʌŋktə/ (Received-Pronunciation)
• (US) audio

Etymology

From function, modeled after factor.

Meanings

1. A function word.
2. (qualifier:object-oriented programming) A function object.
3. A category homomorphism; a morphism from a source category to a target category which maps objects to objects and arrows to arrows (either covariantly or contravariantly), in such a way as to preserve morphism composition and identities.
   • 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 ℱ∈𝒥ℱ the functors ◌̅F: overrightarrow X→◌̅F( overrightarrow X),F⁰: overrightarrow X→F( overrightarrow X)⁰,Fᶜ: overrightarrow X→F( overrightarrow X)ᶜ.
   • 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 Σ_*-objects and we review the relationship between Σ_*-objects and functors. In short, a Σ_*-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→S(M,X), defined by a formula of the form S(M,X)=⨁ ᪲ᵣ₌₀(M(r)⊗X)_(Σᵣ).
   • Given a homotopical category X and a functor u#58;A#92;rightarrowB, 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 Xᵘ#58;Xᴮ#92;rightarrowXᴬ (47.1). 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:
   • In the category of categories #92;mathbf#123;Cat#125; the objects are categories and the morphisms are functors.
4. (qualifier:functional programming) A structure allowing a function to apply within a generic type, in a way that is conceptually similar to a functor in category theory.

Forms

Deriveds

representable functor · functorial · forgetful functor · pseudofunctor · functor category · identity functor · Yoneda functor · profunctor · overfunctor · adjoint functor · contravariant functor · anafunctor · full functor · group functor · subfunctor · underlying functor · faithful functor · bifunctor

Hypernyms

morphism

Translations (23)

ba функтор (category theory: category mapping) · it funtore (category theory: category mapping) · fr foncteur (object-oriented programming: function object) · pt functor (category theory: category mapping) · ja 関手 (category theory: category mapping) · pl funktor (category theory: category mapping) · fi ylinuoli (category theory: category mapping) · kk функтор (category theory: category mapping) · fi funktio-olio (object-oriented programming: function object) · sv funktor (category theory: category mapping) · es functor (category theory: category mapping) · is varpi (category theory: category mapping) · ga feidhmeoir (category theory: category mapping) · de Funktor (category theory: category mapping) · es funtor (category theory: category mapping) · pt funtor (category theory: category mapping) · fi funktori (category theory: category mapping) · ru функтор (category theory: category mapping) · cmn 函子 (category theory: category mapping) · fr foncteur (category theory: category mapping) · hu funktor (category theory: category mapping) · ky функтор (category theory: category mapping) · pl funktor (object-oriented programming: function object)