Classification of exact structures using the Ziegler spectrum
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915762888769536 |
|---|---|
| author | Sauter, Julia |
| author_facet | Sauter, Julia |
| contents | Given an idempotent complete additive category, we show the there is an explicitly constructed topological space such that the lattice of exact substructures is anti-isomorphic to the lattice of closed subsets. In the special case that the additive category has weak cokernels, this topological space is an open subset of the Ziegler spectrum and this is a result of Kevin Schlegel. We also look at some module categories of rings where the Ziegler spectrum is known and calculate the global dimensions of the corresponding exact substructures. Second version contains minor changes to first version. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_02304 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Classification of exact structures using the Ziegler spectrum Sauter, Julia Representation Theory Category Theory 18G25 (Primary), 18G05, 18E45 (Secondary) Given an idempotent complete additive category, we show the there is an explicitly constructed topological space such that the lattice of exact substructures is anti-isomorphic to the lattice of closed subsets. In the special case that the additive category has weak cokernels, this topological space is an open subset of the Ziegler spectrum and this is a result of Kevin Schlegel. We also look at some module categories of rings where the Ziegler spectrum is known and calculate the global dimensions of the corresponding exact substructures. Second version contains minor changes to first version. |
| title | Classification of exact structures using the Ziegler spectrum |
| topic | Representation Theory Category Theory 18G25 (Primary), 18G05, 18E45 (Secondary) |
| url | https://arxiv.org/abs/2506.02304 |