Data.Morphism.Iso

Documentation

data Iso s a b

Constructors

Iso (s a b) (s b a)

Instances

Functor s t f => Functor (Iso s :: α -> α -> Type) (t :: β -> β -> Type) (f :: α -> β)

Defined in Data.Morphism.Iso

Methods

map :: Iso s a b -> t (f a) (f b)

Functor s t f => Functor (Iso s :: α -> α -> Type) (Dual t :: β -> β -> Type) (f :: α -> β)

Defined in Data.Morphism.Iso

Methods

map :: Iso s a b -> Dual t (f a) (f b)

Category s => Category (Iso s :: k -> k -> Type)

Defined in Data.Morphism.Iso

Methods

id :: Iso s a a

(.) :: Iso s b c -> Iso s a b -> Iso s a c

Category s => Groupoid (Iso s :: k -> k -> Type)

Defined in Data.Morphism.Iso

Methods

invert :: Iso s a b -> Iso s b a

(Semigroup (s a b), Semigroup (s b a)) => Semigroup (Iso s a b)

Defined in Data.Morphism.Iso

Methods

(<>) :: Iso s a b -> Iso s a b -> Iso s a b

sconcat :: NonEmpty (Iso s a b) -> Iso s a b

stimes :: Integral b0 => b0 -> Iso s a b -> Iso s a b

(Semigroup (s a b), Semigroup (s b a), Monoid (s a b), Monoid (s b a)) => Monoid (Iso s a b)

Defined in Data.Morphism.Iso

Methods

mempty :: Iso s a b

mappend :: Iso s a b -> Iso s a b -> Iso s a b

mconcat :: [Iso s a b] -> Iso s a b

(Semigroup (s a b), Semigroup (s b a), Group (s a b), Group (s b a)) => Group (Iso s a b)

Defined in Data.Morphism.Iso

Methods

invert :: Iso s a b -> Iso s a b