Year: 2026
Type: preprint
Abstract: Let \(\cB\) be an abelian category with enough projective and injective objects, and let $ \cA=\cB\ltimes_η\sF $ be an \(η\)-extension induced by a right exact endofunctor \(\sF\). We introduce uniform image-nilpotence for \(η\)-extensions and characterize it in terms of the nilpotence of the associative natural transformation \(η:\sF^2\to\sF\). Using the associated \(η\)-Loewy filtration, we prove a lifting theorem for right \(n\)-cotorsion pairs over image-nilpotent \(η\)-extensions and establish a corresponding completeness theorem. As applications, our results recover and unify related constructions for split nilpotent ring extensions, comma categories, formal triangular matrix rings, Morita context rings and classical trivial extensions.
Source: arXiv (Cornell University)
Authors: Liu, Dajun, Gao, Hanpeng
Institution: Anhui University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7215035749