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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 of the relevant ambient category . The recent tools of extriangulated and higher-exangulated categories have permitted some conditions on the subcategory 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.

Publication Type:	Article
Additional Information:	This is an open access article distributed under the terms of the Creative Commons CC-BY license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Publisher Keywords:	Contravariantly finite subcategory, d-abelian category, d-cluster tilting, d-exact category, Generating subcategory, Grothendieck group, Index
Subjects:	Q Science > QA Mathematics
Departments:	School of Science & Technology School of Science & Technology > Department of Mathematics
SWORD Depositor:	Symplectic Administrator

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