Control.Category.Braided

Documentation

class Associative k p => Braided k p where

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

associate . braid . associate = second braid . associate . first braid
disassociate . braid . disassociate = first braid . disassociate . second braid

If the category is Monoidal the following laws should be satisfied

idr . braid = idl
idl . braid = idr

If the category is Comonoidal the following laws should be satisfied

braid . coidr = coidl
braid . coidl = coidr

Methods

braid :: k (p a b) (p b a)

Instances

Braided (->) Either

Braided (->) (,)

class Braided k p => Symmetric k p

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

swap . swap = id

Instances

Symmetric (->) Either

Symmetric (->) (,)

swap :: Symmetric k p => k (p a b) (p b a)