A remark on the additivity of traces in triangulated categories
Shahram Biglari
TL;DR
This paper explores the conditions under which the additivity of traces in tensor triangulated categories can be extended beyond identity endomorphisms, building on May's foundational work.
Contribution
It introduces additional conditions on coefficients that strengthen the additivity results of traces in triangulated categories.
Findings
Extended additivity results under new coefficient conditions
Built upon May's established additivity for identity endomorphisms
Provided a framework for stronger trace additivity in tensor triangulated categories
Abstract
The additivity of traces in certain tensor triangulated categories for endomorphisms of finite order of distinguished triangles is investigated. For the identity endomorphism this has been fully established by J. P. May ("The additivity of traces in triangulated categories", Adv. Math., 2001, 163, 34-73). By imposing extra conditions on the coefficients we show how May's result implies a stronger additivity.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra