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.
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