category-0.2.4.1: Categorical types and classes

Safe HaskellNone
LanguageHaskell2010

Control.Category.Groupoid

Synopsis

Documentation

class Category k => Groupoid k where Source #

Category where every morphism is iso

Laws:

id = f . invert f
id = invert f . f

Methods

invert :: k a b -> k b a Source #

Instances
Category s => Groupoid (Iso s :: k -> k -> Type) Source # 
Instance details

Defined in Data.Morphism.Iso

Methods

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

Groupoid k2 => Groupoid (Dual k2 :: k1 -> k1 -> Type) Source # 
Instance details

Defined in Control.Category.Dual

Methods

invert :: Dual k2 a b -> Dual k2 b a Source #

(Semigroup a, Group a) => Groupoid (Const2 a :: k -> k -> Type) Source # 
Instance details

Defined in Control.Category.Const2

Methods

invert :: Const2 a a0 b -> Const2 a b a0 Source #

Groupoid s => Groupoid (NT s :: (k1 -> k2) -> (k1 -> k2) -> Type) Source # 
Instance details

Defined in Control.Categorical.Functor

Methods

invert :: NT s a b -> NT s b a Source #