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.

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

PreModularFusionCategory{R,N,I,D₁,D₂} <: UnitaryFusionCategory{R,N,I,D₁} <: FusionRing{R,N,I}

which indicate implementations of fusion rules (Nsymbol), associators (Fsymbol) and braidings (Rsymbol). The naming is such that R indicates the rank, N the amount of non-self-dual objects, I the fusion ring index, such that equal values imply the same objects and fusion rules. D₁ is the category index, enumerating different solutions for Fsymbol of the pentagon equation, while D₂ enumerates different solutions of Rsymbol the hexagon equation.

Objects in these categories are identified with integers ranging from 1 to R, where the unit is always 1. These can then be used as any other Sector for constructing TensorMaps.

using TensorKit, CategoryData
𝒞 = PreModularFusionCategory{2,0,2,0,0}     # 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))