Natural Transformation

A natural transformation is a way of transforming one functor into another while respecting the structure of the categories involved.

Given functors $F,G:\mathcal{C}\to \mathcal{D}$, a natural transformation $\eta :F\Rightarrow G$ assigns to each object $A$ in $\mathcal{C}$ a morphism ${\eta }_A:F(A)\to G(A)$ such that for every morphism $f:A\to B$ in $\mathcal{C}$, the following diagram commutes:

$$G(f)\circ {\eta }_A={\eta }_B\circ F(f)$$

See also

• Functor
• Category
• Monad
• Adjunction