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

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.

Mathematics Subject Classification (2020):

• 18E10
• 16D90
• 16T15

Key words:

• Abelian category
• (dual) Rickart object
• (dual) CS-Rickart object
• extending object
• lifting object
• module
• comodule