Phrase guide

contravariant functor

noun · 1 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

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1

noun

Meaning 1

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).

Definition source: English Wiktionary via Wiktextract

Topics: category-theory, computing, engineering, mathematics, natural-sciences, physical-sciences, sciences

Examples

  • 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;.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

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Across languages

Translations

4 source translations are retained for this English entry.

  • Icelandic: hjávarpi — category theory: functor
  • Icelandic: andbrigður varpi — category theory: functor
  • Icelandic: mótbrigður varpi — category theory: functor
  • Portuguese: functor/funtor contravariante — category theory: functor