Math.QuantumAlgebra.TensorCategory

A module defining classes and example instances of categories and tensor categories

Documentation

class Category 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

Category Cob2

Category Braid

Category SymmetricGroupoid

Category OrientedTangle

Category Tangle

class Category c => TensorCategory c where

Methods

tunit :: Ob c

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

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

Instances

TensorCategory Cob2

TensorCategory Braid

TensorCategory SymmetricGroupoid

TensorCategory OrientedTangle

TensorCategory Tangle

class TensorCategory c => StrictTensorCategory c

class TensorCategory c => WeakTensorCategory c where

Methods

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

lunit :: Ob c -> Ob c

runit :: Ob c -> Ob c

data SymmetricGroupoid

Instances

TensorCategory SymmetricGroupoid

Category SymmetricGroupoid

Eq (Ob SymmetricGroupoid)

Eq (Ar SymmetricGroupoid)

Ord (Ob SymmetricGroupoid)

Ord (Ar SymmetricGroupoid)

Show (Ob SymmetricGroupoid)

Show (Ar SymmetricGroupoid)

data Braid

Instances

TensorCategory Braid

Category Braid

Eq (Ob Braid)

Eq (Ar Braid)

Ord (Ob Braid)

Ord (Ar Braid)

Show (Ob Braid)

Show (Ar Braid)

s :: Int -> Int -> Ar Braid

data Cob2

Instances

TensorCategory Cob2

Category Cob2

Eq (Ob Cob2)

Eq (Ar Cob2)

Ord (Ob Cob2)

Ord (Ar Cob2)

Show (Ob Cob2)

Show (Ar Cob2)

rewrite :: Ar Cob2 -> Ar Cob2