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Suppose $F,G:C\to D$ and $H:D\to E$ are functors and $\alpha:F\to G$ is a natural transformation.Let $H\circ \alpha:H\circ F\to H\circ G$ be the right whiskering $(H\circ \alpha)_A:H(FA)\to H(GA)$ defined by $(H\circ\alpha)_A=H(\alpha_A)$. Now how it follows by naturality of $\alpha$ and functo...
In category theory, a branch of mathematics, a natural transformation provides a way of transforming one functor into another while respecting the internal structure (i.e., the composition of morphisms) of the categories involved. Hence, a natural transformation can be considered to be a "morphism of functors". Indeed, this intuition can be formalized to define so-called functor categories. Natural transformations are, after categories and functors, one of the most fundamental notions of category theory and consequently appear in the majority of its applications.
== Definition ==
If F and G are...
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