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natural transformation


from Wiktionary, Creative Commons Attribution/Share-Alike License

  • n. Given categories C and D and functors F and G both going from C to D, then a transformation η from F to G consists of components ηX:F(X) → G(X), indexed by objects X of C, which are morphisms in D. The transformation is said to be natural if for any arrow f:X → Y in C, the following naturality condition is satisfied: .


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