Stable functors and cohomology theory in abelian categories
Rings and Algebras
2023-10-06 v3
Abstract
In this paper, we first introduce stable functors with respect to a preenveloping/precovering subcategory and investigate some of their properties. Using that we then introduce and study a relative complete cohomology theory in abelian categories. Some properties of the cohomology including vanishing are given. As applications, we give some characterizations of objects of finite homological dimensions including the flat dimension, cotorsion dimension, Gorenstein injective/flat dimension and projectively coresolved Gorenstein flat dimension.
Keywords
Cite
@article{arxiv.2006.13562,
title = {Stable functors and cohomology theory in abelian categories},
author = {Shoutao Guo and Li Liang},
journal= {arXiv preprint arXiv:2006.13562},
year = {2023}
}
Comments
28 pages. To appear in Ark. Mat