HaskellForMaths-0.4.8: 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, target :: Ar c -> Ob c Source

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

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

Methods

fob :: Ob a -> Ob b Source

far :: Ar a -> Ar b 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

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