Relatively divisible and relatively flat objects in exact categories

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Crivei S., KESKİN TÜTÜNCÜ D.

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, vol.20, no.5, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 20 Issue: 5
  • Publication Date: 2021
  • Doi Number: 10.1142/s0219498821500882
  • Journal Name: JOURNAL OF ALGEBRA AND ITS APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Hacettepe University Affiliated: Yes

Abstract

We introduce and study relatively divisible and relatively flat objects in exact categories in the sense of Quillen. For every relative cotorsion pair (A, B) in an exact category C, A coincides with the class of relatively flat objects of C for some relative projectively generated exact structure, while B coincides with the class of relatively divisible objects of C for some relative injectively cogenerated exact structure. We exhibit Galois connections between relative cotorsion pairs in exact categories, relative projectively generated exact structures and relative injectively cogenerated exact structures in additive categories. We establish closure properties and characterizations in terms of the approximation theory.