Control.Bifunctor.Braided

Portability	portable
Stability	experimental
Maintainer	Edward Kmett <ekmett@gmail.com>

Description

Synopsis

class Bifunctor p => Braided p where

braid :: p a b -> p b a

class Braided p => Symmetric p

swap :: Symmetric p => p a b -> p b a

Documentation

class Bifunctor p => Braided p where

Source

A braided (co)(monoidal or associative) category can commute the arguments of its bi-endofunctor. Obeys the laws:

 idr . braid = idl 
 idl . braid = idr 
 braid . coidr = coidl 
 braid . coidl = coidr 
 associate . braid . associate = second braid . associate . first braid 
 coassociate . braid . coassociate = first braid . coassociate . second braid

Methods

braid :: p a b -> p b a

Source

Instances

Braided Either

Braided p => Braided (SwapB p)

(Functor f, Braided p) => Braided (FunctorB f p)

(Functor f, Braided p) => Braided (BiffB p f f)

(Bifunctor p, Braided f, Braided g) => Braided (CompB p f g)

class Braided p => Symmetric p

Source

If we have a symmetric (co)Monoidal category, you get the additional law:

 swap . swap = id

Instances

Symmetric Either

Symmetric p => Symmetric (SwapB p)

(Functor f, Symmetric p) => Symmetric (FunctorB f p)

(Functor f, Symmetric p) => Symmetric (BiffB p f f)

(Bifunctor p, Symmetric f, Symmetric g) => Symmetric (CompB p f g)

swap :: Symmetric p => p a b -> p b a

Source

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