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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2303.14925 |
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| _version_ | 1866911014012846080 |
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| author | Wiggins, Giulian |
| author_facet | Wiggins, Giulian |
| contents | This paper studies abelian categories that can be decomposed into smaller abelian categories via iterated recollements - such a decomposition we call a stratification. Examples include the categories of (equivariant) perverse sheaves and epsilon-stratified categories (in particular highest weight categories) in the sense of Brundan-Stroppel (2018).
We give necessary and sufficient conditions for an abelian category with a stratification to be equivalent to a category of finite dimensional modules of a finite dimensional algebra - this generalizes the main result of Cipriani-Woolf (2022). Furthermore, we give necessary and sufficient conditions for such a category to be epsilon-stratified - this generalizes the characterisation of highest weight categories given by Krause (2017). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_14925 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Stratifications of abelian categories Wiggins, Giulian Representation Theory Category Theory 16D90, 16P10 This paper studies abelian categories that can be decomposed into smaller abelian categories via iterated recollements - such a decomposition we call a stratification. Examples include the categories of (equivariant) perverse sheaves and epsilon-stratified categories (in particular highest weight categories) in the sense of Brundan-Stroppel (2018). We give necessary and sufficient conditions for an abelian category with a stratification to be equivalent to a category of finite dimensional modules of a finite dimensional algebra - this generalizes the main result of Cipriani-Woolf (2022). Furthermore, we give necessary and sufficient conditions for such a category to be epsilon-stratified - this generalizes the characterisation of highest weight categories given by Krause (2017). |
| title | Stratifications of abelian categories |
| topic | Representation Theory Category Theory 16D90, 16P10 |
| url | https://arxiv.org/abs/2303.14925 |