natural transformation
（ plural ）
Quizzes for review
(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).
natural transformation
To prove the equivalence of the two functors, she constructed a natural transformation whose components assign to each object a morphism and whose naturality squares commute for every arrow in the domain.
To prove the equivalence of the two functors, she constructed a natural transformation whose components assign to each object a morphism and whose naturality squares commute for every arrow in the domain.
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