  To every Hopf heap or quantum cotorsor of Grunspan a Hopf algebra of
translations is associated. This translation Hopf algebra acts on the Hopf heap
making it a Hopf-Galois co-object. Conversely, any Hopf-Galois co-object has
the natural structure of a Hopf heap with the translation Hopf algebra
isomorphic to the acting Hopf algebra. It is then shown that this assignment
establishes an equivalence between categories of Hopf heaps and Hopf-Galois
co-objects.
