1. contravariant - Noun
2. contravariant - Adjective
(category theory, of a functor) which reverses composition
(object-oriented programming) Using or relating to contravariance.
(linear algebra, of a vector) Scaling inversely with a change of basis.
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.
A pair of adjoint functors between two partially ordered sets is called a Galois connection (or, if it is contravariant, an antitone Galois connection). Source: Internet
Likewise, cotangent space is a contravariant functor, essentially the composition of the tangent space with the dual space above. Source: Internet
For contravariant functors the corresponding notions would be a functor that takes colimits to limits, or one that takes limits to colimits. Source: Internet
For the individual matrix entries, this transformation law has the form so the tensor corresponding to the matrix of a linear operator has one covariant and one contravariant index: it is of type (1,1). Source: Internet
Given an arbitrary contravariant functor G from C to Set, Yoneda's lemma asserts that : Naming conventions The use of "h A " for the covariant hom-functor and "h A " for the contravariant hom-functor is not completely standard. Source: Internet
However, the later book The geometry of schemes / David Eisenbud, Joe Harris (1998) reverses this and uses "h A " to mean the contravariant hom-functor. Source: Internet