natural transformation

English

Wikipedia

Noun

natural transformation (plural natural transformations)

1. (category theory) 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
   η_X: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: $\eta_Y \circ F(f) = G(f) \circ \eta_X$.

Naturality square

References

• TheCatsters – Natural transformations 1