On the derived dimension of abelian categories

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.

References in corpus (2)

• On the representation dimension of artin algebras
• Derived dimensions of representation-finite algebras

Cited by in corpus (2)

• Radical layer length and syzygy-finite algebras
• Dimensions of triangulated categories with respect to subcategories