The theory of j-operators with application to (weak) liftings of DG modules

TL;DR

This paper provides a comprehensive theoretical analysis of j-operators, leading to new characterizations and unified proofs concerning liftings and weak liftings of DG modules over simple DG algebra extensions.

Contribution

It introduces a detailed study of j-operators that unifies and extends existing results on DG module liftings and weak liftings.

Findings

New characterization of (weak) lifting property of DG modules

Unified proofs of existing lifting results

Enhanced understanding of j-operators in DG algebra context

Abstract

A major part of this paper is devoted to an in-depth study of j-operators and their properties. This study enables us to obtain several results on liftings and weak liftings of DG modules along simple extensions of DG algebras and unify the proofs of the existing results obtained by the authors on these subjects. Finally, we provide a new characterization of the (weak) lifting property of DG modules along simple extensions of DG algebras.