Definition of "functor" in English

noun

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 (either covariantly or contravariantly), in such a way as to preserve morphism composition and identities.

   • In the category of categories #92;mathbf#123;Cat#125; 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 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).

4. (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.