natural transformation

noun

A morphism between a pair of parallel functors such that if each object of the shared domain category subtends a correlated arrow — called a component — in the shared codomain (which arrow represents the difference between applying the second functor and the first functor to the correlated object) then each arrow of the shared domain subtends a commuting square — called a naturality square — between two components (correlated to the domain and codomain of the arrow).

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Meanings

nounnatural transformation (plural natural transformations)

plural natural transformations

  1. category theoryA morphism between a pair of parallel functors such that if each object of the shared domain category subtends a correlated arrow — called a component — in the shared codomain (which arrow represents the difference between applying the second functor and the first functor to the correlated object) then each arrow of the shared domain subtends a commuting square — called a naturality square — between two components (correlated to the domain and codomain of the arrow).

Translations

Finnish luonnollinen muunnos
  • luonnollinen muunnosTranslations
German natürliche Transformation
  • natürliche TransformationTranslations
Polish transformacja naturalna
  • transformacja naturalnaTranslations
Russian естественное преобразование
  • естественное преобразование (jestestvennoje preobrazovanije)Translations
Cite this entry
APA

natural transformation. (n.d.). In WatkinsX Dictionary. Retrieved November 5, 2026, from https://dictionary.watkinsx.com/word/natural%20transformation

MLA

“natural transformation.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/natural%20transformation. Accessed November 5, 2026.

Chicago

WatkinsX Dictionary, s.v. “natural transformation,” accessed November 5, 2026, https://dictionary.watkinsx.com/word/natural%20transformation.

Source: natural transformation on Wiktionary, CC BY-SA 4.0.