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 arrows of C to arrows of D such that any arrow f:X→Y of C is mapped to an arrow 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 arrows (and only identity arrows) are mapped to identity arrows. 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.

Italian: funtore (it) m. Polish: funktor (pl) m. Russian: функтор (ru) Swedish: funktor (sv) c.

Derived terms

• contravariant functor
• representable functor