  We generalize the hierarchy construction to generic 2+1D topological orders
(which can be non-Abelian) by condensing Abelian anyons in one topological
order to construct a new one. We show that such construction is reversible and
leads to a new equivalence relation between topological orders. We refer to the
corresponding equivalent class (the orbit of the hierarchy construction) as
"the non-Abelian family". Each non-Abelian family has one or a few root
topological orders with the smallest number of anyon types. All the Abelian
topological orders belong to the trivial non-Abelian family whose root is the
trivial topological order. We show that Abelian anyons in root topological
orders must be bosons or fermions with trivial mutual statistics between them.
The classification of topological orders is then greatly simplified, by
focusing on the roots of each family: those roots are given by non-Abelian
modular extensions of representation categories of Abelian groups.
