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What (who) is 2-functor - definition
2-functor
MORPHISM BETWEEN 2-CATEGORIES (IN THE 3-CATEGORY OF 2-CATEGORIES)
2-functors
In mathematics, a 2-functor is a morphism between 2-categories. They may be defined formally using enrichment by saying that a 2-category is exactly a Cat-enriched category and a 2-functor is a Cat-functor.
Functor
IN CATEGORY THEORY, A MAPPING BETWEEN CATEGORIES THAT PRESERVES THEIR STRUCTURE (IDENTITY MORPHISMS, COMPOSITION OF MORPHISMS)
Covariant functor; Contravariant functor; Cofunctor; Functorial; Functors; Functoriality; Endofunctor; Bifunctor; Covariance and contravariance of functors; Identity functor; Multifunctor; Functor (category theory); Covariance (categories); Opposite functor; Constant functor; Selection functor; Category homomorphism; Dual functor; Covariance and contravariance (category theory)
In mathematics, specifically category theory, a functor is a [between categories]. Functors were first considered in [[algebraic topology, where algebraic objects (such as the fundamental group) are associated to topological spaces, and maps between these algebraic objects are associated to continuous maps between spaces.
functor
IN CATEGORY THEORY, A MAPPING BETWEEN CATEGORIES THAT PRESERVES THEIR STRUCTURE (IDENTITY MORPHISMS, COMPOSITION OF MORPHISMS)
Covariant functor; Contravariant functor; Cofunctor; Functorial; Functors; Functoriality; Endofunctor; Bifunctor; Covariance and contravariance of functors; Identity functor; Multifunctor; Functor (category theory); Covariance (categories); Opposite functor; Constant functor; Selection functor; Category homomorphism; Dual functor; Covariance and contravariance (category theory)
In category theory, a functor F is an operator on types. F
is also considered to be a polymorphic operator on functions
with the type
F : (a -> b) -> (F a -> F b).
Functors are a generalisation of the function "map". The
type operator in this case takes a type T and returns type
"list of T". The map function takes a function and applies it
to each element of a list.
(1995-02-07)
