Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.05356 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909380481384448 |
|---|---|
| author | Wang, Xi Yao, Hailou Shen, Lei |
| author_facet | Wang, Xi Yao, Hailou Shen, Lei |
| contents | We study the $λ$-pure global dimension of a Grothendieck category $\cal A$, and provide two different applications about this dimension. We obtain that if the $λ$-pure global dimension $\plgldA<\infty$, then (1) The ordinary bounded derived category (where $\cal A$ has enough projective objects) and the bounded $λ$-pure one differ only by a homotopy category; (2) The $λ$-pure singularity category $\DlsgA =0$. At last, we explore the reason why the general construction of classic Buchweitz-Happel Theorem is not feasible for $λ$-pure one. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_05356 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lambda-pure global dimension of Grothendieck categories and some applications Wang, Xi Yao, Hailou Shen, Lei Category Theory We study the $λ$-pure global dimension of a Grothendieck category $\cal A$, and provide two different applications about this dimension. We obtain that if the $λ$-pure global dimension $\plgldA<\infty$, then (1) The ordinary bounded derived category (where $\cal A$ has enough projective objects) and the bounded $λ$-pure one differ only by a homotopy category; (2) The $λ$-pure singularity category $\DlsgA =0$. At last, we explore the reason why the general construction of classic Buchweitz-Happel Theorem is not feasible for $λ$-pure one. |
| title | Lambda-pure global dimension of Grothendieck categories and some applications |
| topic | Category Theory |
| url | https://arxiv.org/abs/2411.05356 |