Pure-direct-injective objects in Grothendieck categories

TOKSOY S. E., Yiğit A.

Sao Paulo Journal of Mathematical Sciences, cilt.17, sa.2, ss.831-849, 2023 (Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 17 Sayı: 2
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1007/s40863-022-00347-3
  • Dergi Adı: Sao Paulo Journal of Mathematical Sciences
  • Derginin Tarandığı İndeksler: Scopus
  • Sayfa Sayıları: ss.831-849
  • Anahtar Kelimeler: Pure-direct-injective object, Direct-injective object, Grothendieck category, Abelian category, Module category, Comodule category
  • Hacettepe Üniversitesi Adresli: Evet

Özet

© 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.