Transfer of splitness with respect to a fully invariant short exact sequence in abelian categories

Crivei S., KESKİN TÜTÜNCÜ D., Tribak R.

COMMUNICATIONS IN ALGEBRA, vol.48, no.6, pp.2639-2654, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 48 Issue: 6
  • Publication Date: 2020
  • Doi Number: 10.1080/00927872.2020.1721732
  • Journal Name: COMMUNICATIONS IN ALGEBRA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.2639-2654
  • Hacettepe University Affiliated: Yes

Abstract

We study the transfer via functors between abelian categories of the (dual) relative splitness of objects with respect to a fully invariant short exact sequence. We mainly consider fully faithful functors and adjoint pairs of functors. We deduce applications to Grothendieck categories, (graded) module categories and comodule categories.