# natural transformation

Definition from Wiktionary, the free dictionary

## English[edit]

### Noun[edit]

**natural transformation** (*plural* **natural transformations**)

- (category theory) A morphism between a pair of parallel functors such that if each object of the shared domain category subtends a correlated arrow — called a
*component*— in the shared codomain (which arrow represents the difference between applying the second functor and the first functor to the correlated object) then each arrow of the shared domain subtends a commuting square — called a*naturality square*— between two*components*(correlated to the domain and codomain of the arrow).