contravariant

== English == === Etymology === From contra- + variant. === Pronunciation === === Adjective === contravariant (not comparable) (category theory, of a functor) Which reverses the order of morphism composition: formally, which associates each morphism f : X → Y {\displaystyle f:X\to Y} to a morphism F ( f ) : F ( Y ) → F ( X ) {\displaystyle F(f):F(Y)\to F(X)} . Antonym: covariant (object-oriented programming) Using or relating to contravariance. (linear algebra, of a vector) Scaling inversely with a change of basis. ==== Derived terms ==== ==== Translations ==== === Noun === contravariant (plural contravariants) (algebra) A bihomogeneous polynomial in dual variables of x, y, ... and the coefficients of some homogeneous form in x, y, ... that is invariant under some group of linear transformations. ==== Translations ====