Copyright	(C) 2011-2015 Edward Kmett
License	BSD-style (see the file LICENSE)
Maintainer	Edward Kmett <ekmett@gmail.com>
Stability	provisional
Portability	polykinds
Safe Haskell	Trustworthy
Language	Haskell2010

Data.Groupoid

Description

Synopsis

class Semigroupoid k => Groupoid k where
- inv :: k a b -> k b a

Documentation

class Semigroupoid k => Groupoid k where Source #

semigroupoid with inverses. This technically should be a category with inverses, except we need to use Ob to define the valid objects for the category

Methods

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

Instances

Instances details

Groupoid ((:~:) :: k -> k -> Type) Source #
Instance details Defined in Data.Groupoid Methods inv :: forall (a :: k0) (b :: k0). (a :~: b) -> b :~: a Source #
Groupoid (Coercion :: k -> k -> Type) Source #
Instance details Defined in Data.Groupoid Methods inv :: forall (a :: k0) (b :: k0). Coercion a b -> Coercion b a Source #
Groupoid ((:~~:) :: k -> k -> Type) Source #
Instance details Defined in Data.Groupoid Methods inv :: forall (a :: k0) (b :: k0). (a :~~: b) -> b :~~: a Source #
Semigroupoid k2 => Groupoid (Iso k2 :: k1 -> k1 -> Type) Source #
Instance details Defined in Data.Isomorphism Methods inv :: forall (a :: k) (b :: k). Iso k2 a b -> Iso k2 b a Source #
Groupoid k2 => Groupoid (Dual k2 :: k1 -> k1 -> Type) Source #
Instance details Defined in Data.Groupoid Methods inv :: forall (a :: k) (b :: k). Dual k2 a b -> Dual k2 b a Source #