functor

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.Examples: "In the category of categories, #92;mathbb#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."; "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)."

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.