Relative projectivity and relative injectivity in the category of Doi-Hopf modules II

Abstract

Let k be a field, A a right H-comodule algebra and C a right H-module coalgebra with a fixed grouplike element. We generalize the Fundamental Theorem of (A, H)-Hopf modules to (H, A, C)-Doi-Hopf modules. We also give sufficient conditions for an (H, A, C)-Doi-Hopf module to be injective as a C-comodule.