Morphisms of relative Hopf modules, smash products, and duality (Q1305442)

Let \(H\) be a Hopf \(k\)-algebra, projective over \(k\), \(A\) a right \(H\)-comodule algebra and \({\mathcal M}_A^H\) the category of right \((H,A)\)-Hopf modules. The authors investigate the structure of the space of morphisms between objects of \({\mathcal M}_A^H\). The main result of this paper generalizes a theorem of \textit{H.-J.~Schneider} [in Advances in Hopf algebras, Lect. Notes Pure Appl. Math. 158, 267-297 (1994; Zbl 0817.16017)], obtained in the case when \(H\) is finite dimensional and \(A\) is an \(H\)-Galois extension of its coinvariants. Several duality theorems are obtained as corollaries, some of them extending known results, and a special attention is given to the case when \(H\) is co-Frobenius.