  To a graded finite-rank matrix factorisation of the difference of two
homogeneous potentials one can assign two numbers, the left and right quantum
dimension. The existence of such a matrix factorisation with non-zero quantum
dimensions defines an equivalence relation between potentials, giving rise to
non-obvious equivalences of categories.
  Restricted to ADE singularities, the resulting equivalence classes of
potentials are those of type {A_{d-1}} for d odd, {A_{d-1},D_{d/2+1}} for d
even but not in {12,18,30}, and {A_{11}, D_7, E_6}, {A_{17}, D_{10}, E_7} and
{A_{29}, D_{16}, E_8}. This is the result expected from two-dimensional
rational conformal field theory, and it directly leads to new descriptions of
and relations between the associated (derived) categories of matrix
factorisations and Dynkin quiver representations.
