RELATIVE PROJECTIVITY AND RELATIVE INJECTIVITY IN THE CATEGORY OF DOI–HOPF MODULES

Abstract

Let k be a field, H be a Hopf algebra, A be a right H-comodule algebra and C be a right H-module coalgebra. We extend to the category of (H, A, C)-Doi–Hopf modules a result of Doi on projectivity of every relative (A, H)-Hopf module as an A-module. We also extend the Fundamental Theorem of [C, H]-Hopf modules due to Doi to the category of (H, A, C)-Doi–Hopf modules. Then we discuss relative projectivity and relative injectivity in this category.