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Higher Cotorsion Pairs on Image-Nilpotent η-Extensions
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:sF2→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
@misc{liu2026higher,
title = {{Higher Cotorsion Pairs on Image-Nilpotent \(η\)-Extensions}},
author = {Dajun Liu and Hanpeng Gao},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.39003},
eprint = {2609.39003},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.39003},
}
RIS
TY - UNPB
TI - Higher Cotorsion Pairs on Image-Nilpotent η-Extensions
AU - Dajun Liu
AU - Hanpeng Gao
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.39003
UR - https://arxiv.org/abs/2609.39003
AB - 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→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.
ER -