Finiteness of homological dimensions in triangulated categories
Representation Theory
2026-04-14 v1 Category Theory
Abstract
In a general triangulated category, the finiteness of the finitistic dimension serves as a prerequisite for a categorical obstruction, via the singularity category, to the existence of bounded -structures. In this paper, we investigate the finitistic, big finitistic, and global dimensions, and establish explicit inequalities that relate these dimensions of the middle category in a recollement of triangulated categories to those of the outer categories. This provides a unified framework for extending some known results on the homological dimensions of ordinary rings to weakly approximable triangulated categories.
Keywords
Cite
@article{arxiv.2604.10478,
title = {Finiteness of homological dimensions in triangulated categories},
author = {Hongxing Chen and Xiaohu Chen and Jinbi Zhang},
journal= {arXiv preprint arXiv:2604.10478},
year = {2026}
}