Higher Cotorsion Pairs on Image-Nilpotent $η$-Extensions

Dajun Liu; Hanpeng Gao

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arXiv · 2609.39003

Higher Cotorsion Pairs on Image-Nilpotent $η$-Extensions

Dajun Liu·Hanpeng Gao

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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.

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BibTeX RIS

Dajun Liu, Hanpeng Gao. 2026-09-30. Higher Cotorsion Pairs on Image-Nilpotent $η$-Extensions. https://arxiv.org/abs/2609.39003

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