HaskellForMaths-0.4.9: Combinatorics, group theory, commutative algebra, non-commutative algebra
Safe HaskellSafe
LanguageHaskell98

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 :: Ar c -> Ob c Source #

target :: Ar c -> Ob c Source #

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

Instances

Instances details
MCategory Cob2 Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

Associated Types

data Ob Cob2 Source #

data Ar Cob2 Source #

MCategory Braid Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

Associated Types

data Ob Braid Source #

data Ar Braid Source #

MCategory FinCard Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

Associated Types

data Ob FinCard Source #

data Ar FinCard Source #

MCategory FinOrd Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

Associated Types

data Ob FinOrd Source #

data Ar FinOrd Source #

MCategory Tangle Source # 
Instance details

Defined in Math.QuantumAlgebra.Tangle

Associated Types

data Ob Tangle Source #

data Ar Tangle Source #

MCategory OrientedTangle Source # 
Instance details

Defined in Math.QuantumAlgebra.OrientedTangle

Associated Types

data Ob OrientedTangle Source #

data Ar OrientedTangle Source #

Num k => MCategory (Vect k) Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

Associated Types

data Ob (Vect k) Source #

data Ar (Vect k) Source #

Methods

id_ :: Ob (Vect k) -> Ar (Vect k) Source #

source :: Ar (Vect k) -> Ob (Vect k) Source #

target :: Ar (Vect k) -> Ob (Vect k) Source #

(>>>) :: Ar (Vect k) -> Ar (Vect k) -> Ar (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

Instances details
MFunctor Braid FinCard Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

MFunctor FinOrd FinCard Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

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 #

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

Instances details
Braided Braid Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

Methods

twist :: Ob Braid -> Ob Braid -> Ar Braid Source #

class Braided c => Symmetric c Source #

data FinOrd Source #

Instances

Instances details
Monoidal FinOrd Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

MCategory FinOrd Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

Associated Types

data Ob FinOrd Source #

data Ar FinOrd Source #

MFunctor FinOrd FinCard Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

Eq (Ob FinOrd) Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

Methods

(==) :: Ob FinOrd -> Ob FinOrd -> Bool

(/=) :: Ob FinOrd -> Ob FinOrd -> Bool

Eq (Ar FinOrd) Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

Methods

(==) :: Ar FinOrd -> Ar FinOrd -> Bool

(/=) :: Ar FinOrd -> Ar FinOrd -> Bool

Ord (Ob FinOrd) Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

Methods

compare :: Ob FinOrd -> Ob FinOrd -> Ordering

(<) :: Ob FinOrd -> Ob FinOrd -> Bool

(<=) :: Ob FinOrd -> Ob FinOrd -> Bool

(>) :: Ob FinOrd -> Ob FinOrd -> Bool

(>=) :: Ob FinOrd -> Ob FinOrd -> Bool

max :: Ob FinOrd -> Ob FinOrd -> Ob FinOrd

min :: Ob FinOrd -> Ob FinOrd -> Ob FinOrd

Ord (Ar FinOrd) Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

Methods

compare :: Ar FinOrd -> Ar FinOrd -> Ordering

(<) :: Ar FinOrd -> Ar FinOrd -> Bool

(<=) :: Ar FinOrd -> Ar FinOrd -> Bool

(>) :: Ar FinOrd -> Ar FinOrd -> Bool

(>=) :: Ar FinOrd -> Ar FinOrd -> Bool

max :: Ar FinOrd -> Ar FinOrd -> Ar FinOrd

min :: Ar FinOrd -> Ar FinOrd -> Ar FinOrd

Show (Ob FinOrd) Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

Methods

showsPrec :: Int -> Ob FinOrd -> ShowS

show :: Ob FinOrd -> String

showList :: [Ob FinOrd] -> ShowS

Show (Ar FinOrd) Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

Methods

showsPrec :: Int -> Ar FinOrd -> ShowS

show :: Ar FinOrd -> String

showList :: [Ar FinOrd] -> ShowS

data Ob FinOrd Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

data Ob FinOrd = FinOrdOb Int
data Ar FinOrd Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

data Ar FinOrd = FinOrdAr Int Int [Int]

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

data FinCard Source #

Instances

Instances details
Monoidal FinCard Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

MCategory FinCard Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

Associated Types

data Ob FinCard Source #

data Ar FinCard Source #

MFunctor Braid FinCard Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

MFunctor FinOrd FinCard Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

Eq (Ob FinCard) Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

Methods

(==) :: Ob FinCard -> Ob FinCard -> Bool

(/=) :: Ob FinCard -> Ob FinCard -> Bool

Eq (Ar FinCard) Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

Methods

(==) :: Ar FinCard -> Ar FinCard -> Bool

(/=) :: Ar FinCard -> Ar FinCard -> Bool

Ord (Ob FinCard) Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

Methods

compare :: Ob FinCard -> Ob FinCard -> Ordering

(<) :: Ob FinCard -> Ob FinCard -> Bool

(<=) :: Ob FinCard -> Ob FinCard -> Bool

(>) :: Ob FinCard -> Ob FinCard -> Bool

(>=) :: Ob FinCard -> Ob FinCard -> Bool

max :: Ob FinCard -> Ob FinCard -> Ob FinCard

min :: Ob FinCard -> Ob FinCard -> Ob FinCard

Ord (Ar FinCard) Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

Methods

compare :: Ar FinCard -> Ar FinCard -> Ordering

(<) :: Ar FinCard -> Ar FinCard -> Bool

(<=) :: Ar FinCard -> Ar FinCard -> Bool

(>) :: Ar FinCard -> Ar FinCard -> Bool

(>=) :: Ar FinCard -> Ar FinCard -> Bool

max :: Ar FinCard -> Ar FinCard -> Ar FinCard

min :: Ar FinCard -> Ar FinCard -> Ar FinCard

Show (Ob FinCard) Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

Methods

showsPrec :: Int -> Ob FinCard -> ShowS

show :: Ob FinCard -> String

showList :: [Ob FinCard] -> ShowS

Show (Ar FinCard) Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

Methods

showsPrec :: Int -> Ar FinCard -> ShowS

show :: Ar FinCard -> String

showList :: [Ar FinCard] -> ShowS

data Ob FinCard Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

data Ob FinCard = FinCardOb Int
data Ar FinCard Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

data Ar FinCard = FinCardAr Int Int [Int]

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

finPerm :: [Int] -> Ar FinCard Source #

data Braid Source #

Instances

Instances details
Braided Braid Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

Methods

twist :: Ob Braid -> Ob Braid -> Ar Braid Source #

Monoidal Braid Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

MCategory Braid Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

Associated Types

data Ob Braid Source #

data Ar Braid Source #

MFunctor Braid FinCard Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

Eq (Ob Braid) Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

Methods

(==) :: Ob Braid -> Ob Braid -> Bool

(/=) :: Ob Braid -> Ob Braid -> Bool

Eq (Ar Braid) Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

Methods

(==) :: Ar Braid -> Ar Braid -> Bool

(/=) :: Ar Braid -> Ar Braid -> Bool

Ord (Ob Braid) Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

Methods

compare :: Ob Braid -> Ob Braid -> Ordering

(<) :: Ob Braid -> Ob Braid -> Bool

(<=) :: Ob Braid -> Ob Braid -> Bool

(>) :: Ob Braid -> Ob Braid -> Bool

(>=) :: Ob Braid -> Ob Braid -> Bool

max :: Ob Braid -> Ob Braid -> Ob Braid

min :: Ob Braid -> Ob Braid -> Ob Braid

Ord (Ar Braid) Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

Methods

compare :: Ar Braid -> Ar Braid -> Ordering

(<) :: Ar Braid -> Ar Braid -> Bool

(<=) :: Ar Braid -> Ar Braid -> Bool

(>) :: Ar Braid -> Ar Braid -> Bool

(>=) :: Ar Braid -> Ar Braid -> Bool

max :: Ar Braid -> Ar Braid -> Ar Braid

min :: Ar Braid -> Ar Braid -> Ar Braid

Show (Ob Braid) Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

Methods

showsPrec :: Int -> Ob Braid -> ShowS

show :: Ob Braid -> String

showList :: [Ob Braid] -> ShowS

Show (Ar Braid) Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

Methods

showsPrec :: Int -> Ar Braid -> ShowS

show :: Ar Braid -> String

showList :: [Ar Braid] -> ShowS

data Ob Braid Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

data Ob Braid = BraidOb Int
data Ar Braid Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

data Ar Braid = BraidAr Int [Int]

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

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

data Vect k Source #

Instances

Instances details
Eq (Ob (Vect k)) Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

Methods

(==) :: Ob (Vect k) -> Ob (Vect k) -> Bool

(/=) :: Ob (Vect k) -> Ob (Vect k) -> Bool

Eq (Ar (Vect k)) Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

Methods

(==) :: Ar (Vect k) -> Ar (Vect k) -> Bool

(/=) :: Ar (Vect k) -> Ar (Vect k) -> Bool

Ord (Ob (Vect k)) Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

Methods

compare :: Ob (Vect k) -> Ob (Vect k) -> Ordering

(<) :: Ob (Vect k) -> Ob (Vect k) -> Bool

(<=) :: Ob (Vect k) -> Ob (Vect k) -> Bool

(>) :: Ob (Vect k) -> Ob (Vect k) -> Bool

(>=) :: Ob (Vect k) -> Ob (Vect k) -> Bool

max :: Ob (Vect k) -> Ob (Vect k) -> Ob (Vect k)

min :: Ob (Vect k) -> Ob (Vect k) -> Ob (Vect k)

Ord (Ar (Vect k)) Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

Methods

compare :: Ar (Vect k) -> Ar (Vect k) -> Ordering

(<) :: Ar (Vect k) -> Ar (Vect k) -> Bool

(<=) :: Ar (Vect k) -> Ar (Vect k) -> Bool

(>) :: Ar (Vect k) -> Ar (Vect k) -> Bool

(>=) :: Ar (Vect k) -> Ar (Vect k) -> Bool

max :: Ar (Vect k) -> Ar (Vect k) -> Ar (Vect k)

min :: Ar (Vect k) -> Ar (Vect k) -> Ar (Vect k)

Show (Ob (Vect k)) Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

Methods

showsPrec :: Int -> Ob (Vect k) -> ShowS

show :: Ob (Vect k) -> String

showList :: [Ob (Vect k)] -> ShowS

Show (Ar (Vect k)) Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

Methods

showsPrec :: Int -> Ar (Vect k) -> ShowS

show :: Ar (Vect k) -> String

showList :: [Ar (Vect k)] -> ShowS

Num k => MCategory (Vect k) Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

Associated Types

data Ob (Vect k) Source #

data Ar (Vect k) Source #

Methods

id_ :: Ob (Vect k) -> Ar (Vect k) Source #

source :: Ar (Vect k) -> Ob (Vect k) Source #

target :: Ar (Vect k) -> Ob (Vect k) Source #

(>>>) :: Ar (Vect k) -> Ar (Vect k) -> Ar (Vect k) Source #

data Ob (Vect k) Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

data Ob (Vect k) = VectOb Int
data Ar (Vect k) Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

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

data Cob2 Source #

Instances

Instances details
Monoidal Cob2 Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

MCategory Cob2 Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

Associated Types

data Ob Cob2 Source #

data Ar Cob2 Source #

Eq (Ob Cob2) Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

Methods

(==) :: Ob Cob2 -> Ob Cob2 -> Bool

(/=) :: Ob Cob2 -> Ob Cob2 -> Bool

Eq (Ar Cob2) Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

Methods

(==) :: Ar Cob2 -> Ar Cob2 -> Bool

(/=) :: Ar Cob2 -> Ar Cob2 -> Bool

Ord (Ob Cob2) Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

Methods

compare :: Ob Cob2 -> Ob Cob2 -> Ordering

(<) :: Ob Cob2 -> Ob Cob2 -> Bool

(<=) :: Ob Cob2 -> Ob Cob2 -> Bool

(>) :: Ob Cob2 -> Ob Cob2 -> Bool

(>=) :: Ob Cob2 -> Ob Cob2 -> Bool

max :: Ob Cob2 -> Ob Cob2 -> Ob Cob2

min :: Ob Cob2 -> Ob Cob2 -> Ob Cob2

Ord (Ar Cob2) Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

Methods

compare :: Ar Cob2 -> Ar Cob2 -> Ordering

(<) :: Ar Cob2 -> Ar Cob2 -> Bool

(<=) :: Ar Cob2 -> Ar Cob2 -> Bool

(>) :: Ar Cob2 -> Ar Cob2 -> Bool

(>=) :: Ar Cob2 -> Ar Cob2 -> Bool

max :: Ar Cob2 -> Ar Cob2 -> Ar Cob2

min :: Ar Cob2 -> Ar Cob2 -> Ar Cob2

Show (Ob Cob2) Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

Methods

showsPrec :: Int -> Ob Cob2 -> ShowS

show :: Ob Cob2 -> String

showList :: [Ob Cob2] -> ShowS

Show (Ar Cob2) Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

Methods

showsPrec :: Int -> Ar Cob2 -> ShowS

show :: Ar Cob2 -> String

showList :: [Ar Cob2] -> ShowS

data Ob Cob2 Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

data Ob Cob2 = O Int
data Ar Cob2 Source # 
Instance details

Defined in Math.QuantumAlgebra.TensorCategory

data Ar Cob2