Pure-direct-projective Objects in Grothendieck Categories

In this paper we study generalizations of the concept of pure-direct-projectivity from module categories to Grothendieck categories. We examine for which categories or under what conditions pure-direct -projective objects are direct-projective, quasi-projective, pure-projective, projective and flat. We investigate classes all of whose objects are pure -direct-projective. We give applications of some of the results to comodule categories.