On the derived dimension of abelian categories

TL;DR

This paper establishes an upper bound on the derived dimension of an abelian category based on a subcategory's properties, with applications in related mathematical contexts.

Contribution

It introduces a new upper bound for the derived dimension of abelian categories using subcategory dimensions, expanding understanding in category theory.

Findings

Derived dimension is bounded above by subcategory dimension under certain conditions

Provides applications demonstrating the bound's utility

Enhances theoretical understanding of abelian category structures

Abstract

We give an upper bound on the dimension of the bounded derived category of an abelian category. We show that if $\CX$ is a sufficiently nice subcategory of an abelian category, then derived dimension of $\CA$ is at most $\CX$-dim$\CA$, provided $\CX$-dim$\CA$ is greater than one. We provide some applications.