In category theory terms the difference between functor and contravariance
is that functor is 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 then , and such that identity morphisms (and only identity morphisms) are mapped to identity morphisms. Note: the functor just described is covariant while contravariance is a functor which reverses composition.
As nouns the difference between functor and contravariance
is that functor is a function word while contravariance is the reversal of the order of data types acted upon by an operator.
functor
Noun
(
en noun)
(grammar) a function word
(computing) a function object
(category theory) 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 then , and such that identity morphisms (and only identity morphisms) are mapped to identity morphisms. Note: the functor just described is covariant.
Hyponyms
* (in category theory) endofunctor
Derived terms
* contravariant functor
* representable functor
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contravariance
English
Noun
(label) The reversal of the order of data types acted upon by an operator
(label) A functor which reverses composition
See also
* covariance
Related terms
* contravariant
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