Noun
(grammar) A function word.
(object-oriented programming) A function object.
(category theory) A category homomorphism; a morphism from a source category to a target category which maps objects to objects and arrows to arrows, in such a way as to preserve domains and codomains (of the arrows) as well as composition and identities.
Hyponym: endofunctor
In the category of categories,
C
A
T
{\displaystyle \mathbb {CAT} }
, the objects are categories and the morphisms are functors.
(functional programming) A structure allowing a function to apply within a generic type, in a way that is conceptually similar to a functor in category theory.
Source: en.wiktionary.orgA continuous map of topological spaces X → Y determines a continuous functor O(Y) → O(X). Source: Internet
A functor F from C to D is a mapping that Jacobson (2009), p. 19, def. 1.2. Source: Internet
A functor G lifts limits of type J if it lifts limits for all diagrams of type J. One can therefore talk about lifting products, equalizers, pullbacks, etc. Finally, one says that G lifts limits if it lifts all limits. Source: Internet
Additive functors If C and D are preadditive categories, then a functor F: C → D is additive if it too is enriched over the category Ab. Source: Internet
Additivity If C and D are preadditive categories and F : C ← D is an additive functor with a right adjoint G : C → D, then G is also an additive functor and the hom-set bijections : are, in fact, isomorphisms of abelian groups. Source: Internet
Alternatively one can observe that the functor that for each group takes the underlying monoid (ignoring inverses) has a left adjoint. Source: Internet