functor

Plural: functors

Noun

• Something that functions; a mapping between categories in mathematics.
• A function word.
• A function object.
• 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.
• A structure allowing a function to apply within a generic type, in a way that is conceptually similar to a functor in category theory.

Examples

• He saw himself as a functor, transforming random tiles into coherent, high-scoring words.
• In the category of categories, #92;mathbb#123;CAT#125;, the objects are categories and the morphisms are functors.