Stable functors and cohomology theory in abelian categories
Shoutao Guo, Li Liang
TL;DR
This paper develops a new framework of stable functors and relative cohomology in abelian categories, providing tools to analyze homological dimensions and their properties.
Contribution
It introduces stable functors with respect to subcategories and establishes a relative cohomology theory, advancing the understanding of homological dimensions in abelian categories.
Findings
Characterizations of objects with finite homological dimensions
Properties and vanishing results of the new cohomology theory
Applications to Gorenstein homological dimensions
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.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology