Transfer of CS-Rickart and dual CS-Rickart properties via functors between abelian categories

TL;DR

This paper investigates how (dual) relative CS-Rickart properties are preserved or transferred through functors between abelian categories, with applications to Grothendieck, module, and comodule categories.

Contribution

It introduces conditions under which (dual) relative CS-Rickart properties transfer via fully faithful and adjoint functors in abelian categories, expanding understanding of their behavior.

Findings

Transfer of (dual) relative CS-Rickart properties via functors is characterized.

Applications demonstrate the transfer in Grothendieck, module, and comodule categories.

Results provide new insights into the structure of abelian categories and their functors.

Abstract

We study the transfer of (dual) relative CS-Rickart properties via functors between abelian categories. We consider fully faithful functors as well as adjoint pairs of functors. We give several applications to Grothendieck categories and, in particular, to (graded) module and comodule categories.