contravariant function
[/ˌkɒntrəˈveəriənt ˈfʌŋkʃən/]
nounfemininepl: contravariant functions / funções contravariantes
função contravariante
1. A function between categories that reverses the direction of morphisms; formally, a functor F: C → D such that for objects X, Y in C and a morphism f: X → Y, we have F(f): F(Y) → F(X), reversing the arrow direction
The fundamental group is a contravariant function from the category of pointed topological spaces to the category of groups.
O grupo fundamental é uma função contravariante da categoria de espaços topológicos apontados para a categoria de grupos.
2. In differential geometry and tensor analysis, a function or tensor whose components transform inversely with respect to coordinate transformations, as opposed to covariant transformations
Contravariant functions in tensor calculus have indices written as superscripts and transform with the inverse Jacobian matrix.
Funções contravariantes no cálculo tensorial têm índices escritos como sobrescritos e se transformam com a matriz jacobiana inversa.
This is specialized mathematical terminology used primarily in academic and research contexts within mathematics, theoretical physics, and computer science. The term is part of the standard mathematical vocabulary across both Brazilian Portuguese and European Portuguese academic communities, with no significant regional variations in meaning or usage, though historical texts may use alternative terminology.
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