Data.Category.Boolean

2, or the Boolean category. It contains 2 objects, one for true and one for false. It contains 3 arrows, 2 identity arrows and one from false to true.

Documentation

data Fls

data Tru

data Boolean a b where

Constructors

Fls :: Boolean Fls Fls

F2T :: Boolean Fls Tru

Tru :: Boolean Tru Tru

Instances

Category Boolean

Boolean is the category with true and false as objects, and an arrow from false to true.

HasTerminalObject Boolean

True is the terminal object in the Boolean category.

HasInitialObject Boolean

False is the initial object in the Boolean category.

HasBinaryProducts Boolean

Conjunction is the binary product in the Boolean category.

HasBinaryCoproducts Boolean

Disjunction is the binary coproduct in the Boolean category.

CartesianClosed Boolean

Implication makes the Boolean category cartesian closed.

trueProductMonoid :: MonoidObject (ProductFunctor Boolean) Tru

falseCoproductComonoid :: ComonoidObject (CoproductFunctor Boolean) Fls

trueProductComonoid :: ComonoidObject (ProductFunctor Boolean) Tru

falseCoproductMonoid :: MonoidObject (CoproductFunctor Boolean) Fls

trueCoproductMonoid :: MonoidObject (CoproductFunctor Boolean) Tru

falseProductComonoid :: ComonoidObject (ProductFunctor Boolean) Fls

data NatAsFunctor f g where

Constructors

NatAsFunctor :: (Functor f, Functor g, Category c, Category d, Dom f ~ c, Cod f ~ d, Dom g ~ c, Cod g ~ d) => Nat (Dom f) (Cod f) f g -> NatAsFunctor f g

Instances

(Category (Dom f), Category (Cod f)) => Functor (NatAsFunctor f g)

A natural transformation Nat c d is isomorphic to a functor from c :**: 2 to d.