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Control.Category.Braided | Portability | portable | Stability | experimental | Maintainer | Edward Kmett <ekmett@gmail.com> |
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Description |
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Synopsis |
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Documentation |
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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 :: k (p a b) (p b a) | Source |
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| | Instances | Braided Hask Either | Braided Hask Either | Braided Hask (,) | Braided Hask (,) | Braided Hask (Const2 t) | Braided Hask (Const2 t) | Braided Hask p => Braided Hask (Flip p) | Braided Hask p => Braided Hask (Flip p) | (Functor f, Braided Hask p) => Braided Hask (Of f p) | (Functor f, Braided Hask p) => Braided Hask (Of f p) | (Bifunctor p Hask Hask Hask, Braided Hask f, Braided Hask g) => Braided Hask (Comp p f g) | (Bifunctor p Hask Hask Hask, Braided Hask f, Braided Hask g) => Braided Hask (Comp p f g) | (Functor f, Braided Hask p) => Braided Hask (Biff p f f) | (Functor f, Braided Hask p) => Braided Hask (Biff p f f) |
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If we have a symmetric (co)Monoidal category, you get the additional law:
swap . swap = id
| | Instances | Symmetric Hask Either | Symmetric Hask Either | Symmetric Hask (,) | Symmetric Hask (,) | Symmetric Hask (Const2 t) | Symmetric Hask (Const2 t) | Symmetric Hask p => Symmetric Hask (Flip p) | Symmetric Hask p => Symmetric Hask (Flip p) | (Functor f, Symmetric Hask p) => Symmetric Hask (Of f p) | (Functor f, Symmetric Hask p) => Symmetric Hask (Of f p) | (Bifunctor p Hask Hask Hask, Symmetric Hask f, Symmetric Hask g) => Symmetric Hask (Comp p f g) | (Bifunctor p Hask Hask Hask, Symmetric Hask f, Symmetric Hask g) => Symmetric Hask (Comp p f g) | (Functor f, Symmetric Hask p) => Symmetric Hask (Biff p f f) | (Functor f, Symmetric Hask p) => Symmetric Hask (Biff p f f) |
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