README.md

CategoryData

TensorKit.jl extension for low rank unitary fusion categories, using smallRankUnitaryFusionData

This package provides TensorKit's sectortypes for all objects of multiplicity-free (braided) fusion categories up to rank 6. The full list, along with the naming convention can be found in the Anyon Wiki.

Additionally, some specific categories with multiplicities have also been added.

The fusion categories adhere to a hierarchical structure of exported abstract types:

BraidedCategory <: FusionCategory <: FusionRing

which indicate implementations of fusion rules (Nsymbol), associators (Fsymbol) and braidings (Rsymbol).

Objects in these categories are identified with integers ranging from 1 to R, where $R$ is the rank of the category and the identity object is always 1. These can then be used as any other Sector for constructing TensorMaps.

using TensorKit, CategoryData
𝒞 = CategoryData.Fib # Fibonacci category
𝒪 = Object{𝒞}
@show collect(values(𝒪))                    # 1 -> I, 2 -> τ

t = TensorMap(rand, ComplexF64, Vect[𝒪](1 => 2, 2 => 2) ← Vect[𝒪](1 =>2, 2 => 2))