Functor

//ˈfʌŋktə// noun

noun ·Uncommon ·Advanced level

Definitions

Noun
  1. 1
    A function word.
  2. 2
    A function object.
  3. 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."

  4. 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.

Synonyms

All synonyms
function objectfunction objectfunction wordfunctionoidfunctionoid

Example

More examples

"An affine algebraic group over a field k is a representable covariant functor from the category of commutative algebras over k to the category of groups such that the representing algebra is finitely generated."

Etymology

From function, modeled after factor.

Related phrases

Yoneda functoradjoint functorcontravariant functorfaithful functorforgetful functorfull functorfunctor categorygroup functoridentity functorrepresentable functorunderlying functorfunction object

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Data sourced from Wiktionary, WordNet, CMU, and other open linguistic databases. Updated March 2026.