# Three notions of dimension for triangulated categories

## 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.

## Key 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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Source: https://tomesphere.com/paper/1901.09461