contravariant functor

noun

A functor which maps a morphism f:X → Y to a morphism F(f):F(Y) → F(X), such that if h=g∘f, then F(h)=F(f)∘F(g).

“A contravariant functor F#58;#92;mathcal#123;C#125;#92;rightarrow#92;mathcal#123;D#125; is the same as a covariant functor F#58;#92;mathcal#123;C#125;#123;op#125;#92;rightarrow#92;mathcal#123;D#125;.”

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Meanings

nouncontravariant functor (plural contravariant functors)

plural contravariant functors

  1. category theoryA functor which maps a morphism f:X → Y to a morphism F(f):F(Y) → F(X), such that if h=g∘f, then F(h)=F(f)∘F(g).

    A contravariant functor F#58;#92;mathcal#123;C#125;#92;rightarrow#92;mathcal#123;D#125; is the same as a covariant functor F#58;#92;mathcal#123;C#125;#123;op#125;#92;rightarrow#92;mathcal#123;D#125;.

Translations

Icelandic hjávarpi, andbrigður varpi
  • hjávarpicategory theory: functor
  • andbrigður varpicategory theory: functor
  • mótbrigður varpicategory theory: functor
Portuguese functor/funtor contravariante
  • functor/funtor contravariantecategory theory: functor
Cite this entry
APA

contravariant functor. (n.d.). In WatkinsX Dictionary. Retrieved November 4, 2026, from https://dictionary.watkinsx.com/word/contravariant%20functor

MLA

“contravariant functor.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/contravariant%20functor. Accessed November 4, 2026.

Chicago

WatkinsX Dictionary, s.v. “contravariant functor,” accessed November 4, 2026, https://dictionary.watkinsx.com/word/contravariant%20functor.

Source: contravariant functor on Wiktionary, CC BY-SA 4.0.