functor

English

Wikipedia

Noun

functor (plural functors)

1. (grammar) a function word
2. (computing) a function object
3. (mathematics) a structure-preserving mapping between categories: if F is a functor from category C to category D, then F maps objects of C to objects of D and morphisms of C to morphisms of D such that any morphism f:X→Y of C is mapped to a morphism F(f): F(X) → F(Y) of D, such that if $h = g \circ f$ then $F(h) = F(g) \circ F(f)$, and such that identity morphisms (and only identity morphisms) are mapped to identity morphisms. Note: the functor just described is covariant.

Translations

grammar: function word — see function word

computing: function word — see function object

mathematics: a mapping between categories

• Finnish: funktori (fi)
• French: foncteur (fr) m
• German: Funktor (de) m
• Hungarian: funktor (hu)
• Icelandic: varpi (is) m

• Irish: feidhmeoir (ga)
• Italian: funtore (it) m
• Japanese: 関手 (ja) (かんしゅ, kanshu)
• Polish: funktor (pl) m
• Russian: функтор (ru) (funktor)
• Swedish: funktor (sv) c

Derived terms

• contravariant functor
• representable functor