Pure-direct-injective objects in Grothendieck categories

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