Remarks on dimensions of triangulated categories
Takuma Aihara, Ryo Takahashi
TL;DR
This paper investigates the conditions under which locally finite triangulated categories have zero or finite dimension and examines how derived categories can be generated by orthogonal subcategories.
Contribution
It provides new insights into the dimensional properties of triangulated categories and the generation of derived categories by specific subcategories.
Findings
Characterization of when a triangulated category has dimension zero
Criteria for finite representation type in such categories
Analysis of generation of derived categories by orthogonal subcategories
Abstract
In this paper, we explore when a locally finite triangulated category has dimension zero or finite representation type. We also study generation of derived categories by orthogonal subcategories.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology