  A coaction of a Hopf algebra on a unital algebra is called homogeneous if the
algebra of coinvariants equals the ground field. A coaction of a Hopf algebra
on a (not necessarily unital) algebra is called Galois, or principal, or free,
if the canonical map, also known as the Galois map, is bijective. In this
paper, we establish a duality between a particular class of homogeneous
coactions, up to equivariant Morita equivalence, and Galois coactions, up to
isomorphism.
