Safe Haskell	Safe
Language	Haskell98

Math.QuantumAlgebra.TensorCategory

Description

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

Documentation

class MCategory c where Source

Associated Types

data Ob c :: * Source

data Ar c :: * Source

Methods

id_ :: Ob c -> Ar c Source

source, target :: Ar c -> Ob c Source

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

Instances

MCategory Cob2 Source
MCategory Braid Source
MCategory FinCard Source
MCategory FinOrd Source
MCategory OrientedTangle Source
MCategory Tangle Source
Num k => MCategory (Vect k) Source

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

Methods

fob :: Ob a -> Ob b Source

far :: Ar a -> Ar b Source

Instances

MFunctor Braid FinCard Source
MFunctor FinOrd FinCard Source

class MCategory c => Monoidal c where Source

Methods

tunit :: Ob c Source

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

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

Instances

Monoidal Cob2 Source
Monoidal Braid Source
Monoidal FinCard Source
Monoidal FinOrd Source
Monoidal OrientedTangle Source
Monoidal Tangle Source

class Monoidal c => StrictMonoidal c Source

class Monoidal c => WeakMonoidal c where Source

Methods

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

lunit :: Ob c -> Ar c Source

runit :: Ob c -> Ar c Source

class Monoidal c => Braided c where Source

Methods

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

Instances

Braided Braid Source

class Braided c => Symmetric c Source

data FinOrd Source

Instances

Monoidal FinOrd Source
MCategory FinOrd Source
MFunctor FinOrd FinCard Source
Eq (Ob FinOrd) Source
Eq (Ar FinOrd) Source
Ord (Ob FinOrd) Source
Ord (Ar FinOrd) Source
Show (Ob FinOrd) Source
Show (Ar FinOrd) Source
data Ob FinOrd = FinOrdOb Int Source
data Ar FinOrd = FinOrdAr Int Int [Int] Source

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

data FinCard Source

Instances

Monoidal FinCard Source
MCategory FinCard Source
MFunctor Braid FinCard Source
MFunctor FinOrd FinCard Source
Eq (Ob FinCard) Source
Eq (Ar FinCard) Source
Ord (Ob FinCard) Source
Ord (Ar FinCard) Source
Show (Ob FinCard) Source
Show (Ar FinCard) Source
data Ob FinCard = FinCardOb Int Source
data Ar FinCard = FinCardAr Int Int [Int] Source

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

finPerm :: [Int] -> Ar FinCard Source

data Braid Source

Instances

Braided Braid Source
Monoidal Braid Source
MCategory Braid Source
MFunctor Braid FinCard Source
Eq (Ob Braid) Source
Eq (Ar Braid) Source
Ord (Ob Braid) Source
Ord (Ar Braid) Source
Show (Ob Braid) Source
Show (Ar Braid) Source
data Ob Braid = BraidOb Int Source
data Ar Braid = BraidAr Int [Int] Source

t :: Int -> Int -> Ar Braid Source

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

data Vect k Source

Instances

Eq (Ob (Vect k)) Source
Eq (Ar (Vect k)) Source
Ord (Ob (Vect k)) Source
Ord (Ar (Vect k)) Source
Show (Ob (Vect k)) Source
Show (Ar (Vect k)) Source
Num k => MCategory (Vect k) Source
data Ob (Vect k) = VectOb Int Source
data Ar (Vect k) = VectAr Int Int [[Int]] Source

data Cob2 Source

Instances

Monoidal Cob2 Source
MCategory Cob2 Source
Eq (Ob Cob2) Source
Eq (Ar Cob2) Source
Ord (Ob Cob2) Source
Ord (Ar Cob2) Source
Show (Ob Cob2) Source
Show (Ar Cob2) Source
data Ob Cob2 = O Int Source
data Ar Cob2 = Id Int \| Unit \| Mult \| Counit \| Comult \| Par (Ar Cob2) (Ar Cob2) \| Seq (Ar Cob2) (Ar Cob2) Source

rewrite :: Ar Cob2 -> Ar Cob2 Source