Stratifying Systems via Nested Family of Torsion Pairs
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912076086116352 |
|---|---|
| author | Alvares, Edson Ribeiro Santos, Matheus Vinicius dos |
| author_facet | Alvares, Edson Ribeiro Santos, Matheus Vinicius dos |
| contents | In this paper, we introduce the concept of a nested family of torsion pairs and will prove that this concept is strongly related to the existence of stratifying systems. Specifically, every stratifying system induces a nested family of torsion pairs. Moreover, every stratifying system can be obtained as a quotient or submodule of a module that admits a certain direct sum decomposition with respect to the nested family of torsion pairs. Additionally, we present a stratifying system of infinite size that cannot be indexed by $\mathbb{N}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_14016 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stratifying Systems via Nested Family of Torsion Pairs Alvares, Edson Ribeiro Santos, Matheus Vinicius dos Representation Theory Category Theory 16G10, 18E40, 18G20, 16D10, 16G20 (Primary) In this paper, we introduce the concept of a nested family of torsion pairs and will prove that this concept is strongly related to the existence of stratifying systems. Specifically, every stratifying system induces a nested family of torsion pairs. Moreover, every stratifying system can be obtained as a quotient or submodule of a module that admits a certain direct sum decomposition with respect to the nested family of torsion pairs. Additionally, we present a stratifying system of infinite size that cannot be indexed by $\mathbb{N}$. |
| title | Stratifying Systems via Nested Family of Torsion Pairs |
| topic | Representation Theory Category Theory 16G10, 18E40, 18G20, 16D10, 16G20 (Primary) |
| url | https://arxiv.org/abs/2410.14016 |