natural transformation

natural transformation
Given categories C and D and functors F and G both going from C to D, then a transformation &eta; from F to G consists of components &eta;<sub>X</sub>:F(X) &rarr; 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 &rarr; Y in C, the following naturality condition is satisfied: <math> \\eta_Y \\circ F(f) = G(f) \\circ \\eta_X</math>.

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