Finiteness of homological dimensions in triangulated categories
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866911586650685440 |
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| author | Chen, Hongxing Chen, Xiaohu Zhang, Jinbi |
| author_facet | Chen, Hongxing Chen, Xiaohu Zhang, Jinbi |
| contents | 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 $t$-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_10478 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Finiteness of homological dimensions in triangulated categories Chen, Hongxing Chen, Xiaohu Zhang, Jinbi Representation Theory Category Theory 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 $t$-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. |
| title | Finiteness of homological dimensions in triangulated categories |
| topic | Representation Theory Category Theory |
| url | https://arxiv.org/abs/2604.10478 |