Functor
/ˈfʌŋktə/ noun
noun ·Rare ·Advanced level
Definitions
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."
- 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.
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.