natural transformation

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Naturality square between two components, ηX and ηY, of a natural transformation η:F→G. The space between the top and the bottom represents the difference between applying the first and the second functor to objects X, Y, and arrow f of their shared domain.

Noun

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natural transformation (plural natural transformations)

  1. (category theory) 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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