# CategoryData

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

This package currently 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 here.

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 `TensorMap`

s.

using TensorKit, CategoryData
๐ = CategoryData.Fib # Fibonacci category
๐ช = Object{๐}
@show collect(values(๐ช)) # 1 -> I, 2 -> ฯ
t = TensorMap(rand, ComplexF64, Vect[๐ช](1 => 2, 2 => 2) โ Vect[๐ช](1 =>2, 2 => 2))