Murat Kasimov

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Я language (β)

/Я language (β)/Glossary/Functor/

Functor is a mapping between categories. Depends the way functors map morphisms they could be either covariant or contravariant. Covariant functors map morphisms as it is, contravariant functors flip morphisms:

: source a o `AR_` target ( t a ) ( t o ) | covariant : source o a `AR_` target ( t a ) ( t o ) | contravariant

Functors which map from (source) and into (target) the same category are called endo functors.

: target a o `AR_` target ( t a ) ( t o ) | covariant : target o a `AR_` target ( t a ) ( t o ) | contravariant

Functor mapping operators in Я are Yonedified:

`yo` : t a `AR__` target ( source a o ) ( t o ) `ya` : t a `AR__` target ( source o a ) ( t o )

We compose functors by treating one of them as an argument of another one:

`yo'yo` : t ( tt a ) `AR__` target ( source a o ) ( t ( tt o ) ) `yo'ya` : t ( tt a ) `AR__` target ( source o a ) ( t ( tt o ) ) `ya'yo` : t ( tt a ) `AR__` target ( source o a ) ( t ( tt o ) ) `ya'ya` : t ( tt a ) `AR__` target ( source a o ) ( t ( tt o ) )