Stratifications of abelian categories
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).
Cite
@article{arxiv.2303.14925,
title = {Stratifications of abelian categories},
author = {Giulian Wiggins},
journal= {arXiv preprint arXiv:2303.14925},
year = {2025}
}