Math.QuantumAlgebra.TensorCategory

A module defining classes and example instances of categories, monoidal categories and braided categories

Documentation

class MCategory c where

Associated Types

data Ob c :: *

data Ar c :: *

Methods

id_ :: Ob c -> Ar c

source, target :: Ar c -> Ob c

(>>>) :: Ar c -> Ar c -> Ar c

Instances

MCategory Cob2

MCategory Braid

MCategory FinCard

MCategory FinOrd

MCategory OrientedTangle

MCategory Tangle

Num k => MCategory (Vect k)

class (MCategory a, MCategory b) => MFunctor a b where

Methods

fob :: Ob a -> Ob b

far :: Ar a -> Ar b

Instances

MFunctor Braid FinCard

MFunctor FinOrd FinCard

class MCategory c => Monoidal c where

Methods

tunit :: Ob c

tob :: Ob c -> Ob c -> Ob c

tar :: Ar c -> Ar c -> Ar c

Instances

Monoidal Cob2

Monoidal Braid

Monoidal FinCard

Monoidal FinOrd

Monoidal OrientedTangle

Monoidal Tangle

class Monoidal c => StrictMonoidal c

class Monoidal c => WeakMonoidal c where

Methods

assoc :: Ob c -> Ob c -> Ob c -> Ar c

lunit :: Ob c -> Ar c

runit :: Ob c -> Ar c

class Monoidal c => Braided c where

Methods

twist :: Ob c -> Ob c -> Ar c

Instances

Braided Braid

class Braided c => Symmetric c

data FinOrd

Instances

Monoidal FinOrd

MCategory FinOrd

MFunctor FinOrd FinCard

Eq (Ob FinOrd)

Eq (Ar FinOrd)

Ord (Ob FinOrd)

Ord (Ar FinOrd)

Show (Ob FinOrd)

Show (Ar FinOrd)

data Ob FinOrd = FinOrdOb Int

data Ar FinOrd = FinOrdAr Int Int [Int]

finOrdAr :: Int -> Int -> [Int] -> Ar FinOrd

data FinCard

Instances

Monoidal FinCard

MCategory FinCard

MFunctor Braid FinCard

MFunctor FinOrd FinCard

Eq (Ob FinCard)

Eq (Ar FinCard)

Ord (Ob FinCard)

Ord (Ar FinCard)

Show (Ob FinCard)

Show (Ar FinCard)

data Ob FinCard = FinCardOb Int

data Ar FinCard = FinCardAr Int Int [Int]

finCardAr :: Int -> Int -> [Int] -> Ar FinCard

finPerm :: [Int] -> Ar FinCard

data Braid

Instances

Braided Braid

Monoidal Braid

MCategory Braid

MFunctor Braid FinCard

Eq (Ob Braid)

Eq (Ar Braid)

Ord (Ob Braid)

Ord (Ar Braid)

Show (Ob Braid)

Show (Ar Braid)

data Ob Braid = BraidOb Int

data Ar Braid = BraidAr Int [Int]

t :: Int -> Int -> Ar Braid

t' :: Int -> Int -> Ar Braid

data Vect k

Instances

Eq (Ob (Vect k))

Eq (Ar (Vect k))

Ord (Ob (Vect k))

Ord (Ar (Vect k))

Show (Ob (Vect k))

Show (Ar (Vect k))

Num k => MCategory (Vect k)

data Ob (Vect k) = VectOb Int

data Ar (Vect k) = VectAr Int Int [[Int]]

data Cob2

Instances

Monoidal Cob2

MCategory Cob2

Eq (Ob Cob2)

Eq (Ar Cob2)

Ord (Ob Cob2)

Ord (Ar Cob2)

Show (Ob Cob2)

Show (Ar Cob2)

data Ob Cob2 = O Int

data Ar Cob2

• = Id Int
• | Unit
• | Mult
• | Counit
• | Comult
• | Par (Ar Cob2) (Ar Cob2)
• | Seq (Ar Cob2) (Ar Cob2)

rewrite :: Ar Cob2 -> Ar Cob2