Pure-direct-injective objects in Grothendieck categories

TOKSOY S. E., Yiğit A.

Sao Paulo Journal of Mathematical Sciences, 2022 (Scopus) identifier

  • Publication Type: Article / Article
  • Publication Date: 2022
  • Doi Number: 10.1007/s40863-022-00347-3
  • Journal Name: Sao Paulo Journal of Mathematical Sciences
  • Journal Indexes: Scopus
  • Keywords: Abelian category, Comodule category, Direct-injective object, Grothendieck category, Module category, Pure-direct-injective object
  • Hacettepe University Affiliated: Yes


© 2022, Instituto de Matemática e Estatística da Universidade de São Paulo.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.