This PR is a work in progress for a refactor of GradedUnitRange, following the interface defined in https://gist.github.com/ogauthe/b22450c66b5ad937db47b49cd8e6b1cb.

This implementation does not use LabelledNumbers. Instead it is based on a "full range", which take into account multi-dimensional irreps:

struct SectorUnitRange{T,Sector,Range<:AbstractUnitRange{T}} <: AbstractUnitRange{T}
  nondual_sector::Sector
  full_range::Range
  isdual::Bool
end

const SectorOneTo{T,Sector,Range} = SectorUnitRange{T,Sector,Base.OneTo{T}}

struct GradedUnitRange{
  T,BlockLasts,BR<:AbstractBlockedUnitRange{T,BlockLasts},SUR<:SectorOneTo{T}
} <: AbstractGradedUnitRange{T,BlockLasts}
  sectors::Vector{SUR}
  range::BR
end

const GradedOneTo{T,BlockLasts,BR,SUR} = GradedUnitRange{T,BlockLasts,BR,SUR} where {BR<:BlockedOneTo}

There is still work to be done to update all methods. Some interface choices are open for discussion (accessors...). However I realized there is an issue with the current plan: it cannot handle non-group categories. Indeed the objective is to have length(full_range) == quantum_dimension and to iterate on the axis to reach any state. This is not compatible with non-integer quantum dimension. Concerning structure, Base.OneTo, BlockedUnitRange and BlockedOneTo impose Integer eltype, we cannot directly use them with e.g. Fibonacci.

The problem is serious, there is a real incompatibility between iterating on an axis and non-integer length. There are several possibilities:

• conservative: drop length = quantum_dimension and keep the current length = multiplicity convention.
• radical: drop non-group category. A full implementation requires additional features (braiding) that are not currently planned, we would not loose functionality.
• intermediate: store (integer based) multiplicity axes in the implementation and have methods that may return float. This does not solve the question "how to iterate on such an axis`.