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arXiv · 2303.14925

Stratifications of abelian categories

Giulian Wiggins
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Abstract

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).

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BibTeXRIS

Giulian Wiggins. 2023-03-27. Stratifications of abelian categories. https://arxiv.org/abs/2303.14925

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