Definition. Natural Transformation [math-000N]

Let $\mathcal{C}$ and $\mathcal{D}$ be categories, let $F, G : \mathcal{C} \to \mathcal{D}$ be functors. A natural transformation $\alpha : F \Rightarrow G$ is a function consists of

1. For each $X \in \mathcal{C}$ , there is a morphism $\alpha_X : F(X) \to G(X)$ in $\mathcal{D}$ , called the $X$ -component of $\alpha$
2. For every morphism $f : X \to Y$ in $\mathcal{C}$ , there is a commute diagram