The index in d-exact categories
Year: 2025
Type: article
Abstract: Starting from its original definition in module categories with respect to projective modules, the index has played an important role in various aspects of homological algebra, categorification of cluster algebras and K -theory. In the last few years, the notion of index has been generalised to several different contexts in (higher) homological algebra, typically with respect to a (higher) cluster-tilting subcategory X of the relevant ambient category C . The recent tools of extriangulated and higher-exangulated categories have permitted some conditions on the subcategory X to be relaxed. In this paper, we introduce the index with respect to a generating, contravariantly finite subcategory of a d -exact category that has d -kernels. We show that our index has the important property of being additive on d -exact sequences up to an error term.
Source: Journal of Algebra
Authors: Francesca Fedele, Peter Jørgensen, Amit Shah
Institutions: University of Leeds, Aarhus University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,310
OpenAlex ID: W4413982564