Three notions of dimension for triangulated categories
Alexey Elagin, Valery A. Lunts
TL;DR
This paper explores three different concepts of dimension in triangulated categories, analyzing their properties, relationships, and open questions to deepen understanding of their mathematical structure.
Contribution
It introduces and compares Rouquier, diagonal, and Serre dimensions, highlighting their properties and open problems in the study of triangulated categories.
Findings
Basic properties of the three dimensions are established.
Comparisons between the dimensions are discussed.
Open problems related to these dimensions are presented.
Abstract
In this note we discuss three notions of dimension for triangulated categories: Rouquier dimension, diagonal dimension and Serre dimension. We prove some basic properties of these dimensions, compare them and discuss open problems.
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