Editing Natural transformation (section)

{{Redirect|Natural operation|the natural sum and natural product on ordinals|Ordinal arithmetic#Natural operations}}
{{About|natural transformations in category theory|the natural competence of bacteria to take up foreign DNA|Genetic transformation|other uses|Transformation (mathematics) (disambiguation)}}
{{short description|Central object of study in category theory}}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 [[morphism]]s) of the [[Category (mathematics)|categories]] involved. Hence, a natural transformation can be considered to be a "morphism of functors". Informally, the notion of a natural transformation states that a particular map between functors can be done consistently over an entire category.

Indeed, this intuition can be formalized to define so-called [[functor category|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.