  We introduce the notion of H-equivariant Morita-Takeuchi theory for
coalgebras with symmetries given by a Hopf algebra H. A cohomology theory is
introduced which classifies the possible lifts of coactions on coalgebras to
corresponding comodules. An equivariant Picard groupoid is defined and its
connection to the developed cohomology theory investigated.

Representation Theory;Rings and Algebras