Rickart and dual Rickart objects in abelian categories: transfer via functors

TL;DR

This paper investigates how (dual) relative Rickart properties transfer through functors in abelian categories, leading to new insights into (dual) relative Baer properties and applications in various algebraic contexts.

Contribution

It introduces methods for transferring (dual) relative Rickart and Baer properties via functors, expanding understanding in abelian and related categories.

Findings

Transfer of (dual) relative Rickart properties via functors

Transfer of (dual) relative Baer property in abelian categories

Applications to Grothendieck, comodule, and graded module categories

Abstract

We study the transfer of (dual) relative Rickart properties via functors between abelian categories, and we deduce the transfer of (dual) relative Baer property. We also give applications to Grothendieck categories, comodule categories and (graded) module categories, with emphasis on endomorphism rings.