HaskellForMaths-0.4.7: Combinatorics, group theory, commutative algebra, non-commutative algebra

Safe HaskellSafe-Inferred
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, target :: Ar c -> Ob c Source

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

Instances

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

Methods

fob :: Ob a -> Ob b Source

far :: Ar a -> Ar b Source

Instances

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

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

class Braided c => Symmetric c Source

data FinOrd Source

Instances

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

data FinCard Source

Instances

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

finPerm :: [Int] -> Ar FinCard Source

data Braid Source

Instances

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

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

data Vect k Source

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 Source

Instances

rewrite :: Ar Cob2 -> Ar Cob2 Source