Data.Category.Hask

Documentation

type Hask = (->)

data EndoHask f

EndoHask is a wrapper to turn instances of the Functor class into categorical functors.

Constructors

EndoHask

Instances

Functor f => VoidColimit (Alg (EndoHask f))

Functor f => FunctorA (EndoHask f) a b

data Zero

Any empty data type is an initial object in Hask.

magic :: Zero -> a

initObjInHask :: Limit (Id (->)) Zero

An alternative way to define the initial object.

termObjInHask :: Colimit (Id (->)) ()

An alternative way to define the terminal object.

data ProdInHask

The product functor, Hask^2 -> Hask

Constructors

ProdInHask

Instances

(Dom f ~ Pair, Cod f ~ (->), Dom g ~ Pair, Cod g ~ (->)) => FunctorA ProdInHask f g

prodInHaskAdj :: Adjunction (Diag Pair (->)) ProdInHask

The product functor is right adjoint to the diagonal functor.

data CoprodInHask

The coproduct functor, Hask^2 -> Hask

Constructors

CoprodInHask

Instances

(Dom f ~ Pair, Cod f ~ (->), Dom g ~ Pair, Cod g ~ (->)) => FunctorA CoprodInHask f g

coprodInHaskAdj :: Adjunction CoprodInHask (Diag Pair (->))

The coproduct functor is left adjoint to the diagonal functor.