Stable functors and cohomology theory in abelian categories

Li Liang (Department of Mathematics, Lanzhou Jiaotong University, Lanzhou, China; and Gansu Provincial Research Center for Basic Disciplines of Mathematics & Statistics, Lanzhou, China)

Abstract

In this paper, we first introduce stable functors with respect to a pre-enveloping / pre-covering 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

stable functor, complete/Tate cohomology, special preenveloping/ precovering subcategory

2010 Mathematics Subject Classification

18G10, 18G15, 18G25

Full Text (PDF format)

Received 16 January 2023

Received revised 4 June 2023

Accepted 14 June 2023

Published 1 June 2024