Murat Kasimov

More about me

Я language (β)

/Я language (β)/Glossary/Natural Transformation/

Functor is a mapping between categories, natural transformation is a mapping between functors. Only functors of the same variance could form a natural transformation.

Natural transformation between covariant functors:

: from a o `AR_` into ( t a ) ( t o ) | covariant functor : from a o `AR_` into ( tt a ) ( tt o ) | covariant functor : from a o `AR_` into ( t a ) ( tt o ) | natural transformation

Natural transformation between contravariant functors:

: from o a `AR_` into ( t a ) ( t o ) | contravariant functor : from o a `AR_` into ( tt a ) ( tt o ) | contravariant functor : from o a `AR_` into ( t a ) ( tt o ) | natural transformation

Component of a natural transformation is a mapping between functors with identity morphism:

: into ( t i ) ( tt i ) | component of a natural transformation

There are type operators available for components in Arrow and Scope categories:

: t `C'AR` tt | component of a natural transformation in Arrow : t `C'AT` tt | component of a natural transformation in Scope