functor

A function word.

Noun

  1. A function word.
  2. 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.
    • 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...
    • 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...

    Hypernyms: morphism

  4. A structure allowing a function to apply within a generic type, in a way that is conceptually similar to a functor in category theory.

Origin

From function, modeled after factor.

Forms

functors

Derived

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