Higher Cotorsion Pairs on Image-Nilpotent \(η\)-Extensions

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 associ