F-Baer objects with respect to a fully invariant short exact sequence in abelian categories

Abstract

We introduce and study (dual) relative F-Baer objects as specializations of (dual) relative split objects with respect to a fully invariant short exact sequence in $AB{3}^{*}$ (AB3) abelian categories. We analyze their relationship with (dual) relative Baer objects, and we study direct summands and direct sums of (dual) relative F-Baer objects. We give applications to module and comodule categories.

Keywords:

• Abelian category
• (dual) (strongly) Baer object
• (dual) (strongly) F-Baer object
• fully invariant short exact sequence

2020 Mathematics Subject Classification:

• 18E10
• 18E15
• 16D90