Finite dimensional Hopf algebras coacting on coalgebras (Q1281157)

If \(C\) is a left \(H\)-comodule coalgebra over a finite dimensional Hopf algebra \(H\), then let \(C\rtimes H\) be the cosmash product and \(R\) the quotient coalgebra \(C/CH^{*+}\). The authors study the question when \(C/R\) is \(H^*\)-co-Galois, show that there is a category equivalence between the category of comodules \(^R{\mathcal M}\) and the category of Hopf comodules \(^{(C,H)}{\mathcal M}\) (\(\cong{^C{\mathcal M}_{H^*}}\)), and study properties of the cotrace map. They obtain duals of a number of known results.