  Higher cluster categories were recently introduced as a generalization of
cluster categories.
  This paper shows that in Dynkin types A and D, half of all higher cluster
categories are actually just quotients of cluster categories. The other half
can be obtained as quotients of 2-cluster categories, the "lowest" type of
higher cluster categories.
  Hence, in Dynkin types A and D, all higher cluster phenomena are implicit in
cluster categories and 2-cluster categories. In contrast, the same is not true
in Dynkin type E.
