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arXiv · 2410.14016

Stratifying Systems via a Nested Family of Torsion Pairs

Edson Ribeiro Alvares·Matheus Vinicius dos Santos
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Abstract

In this paper, we introduce the notion of a nested family of torsion pairs. We show that every stratifying system induces a nested family of torsion pairs and, conversely, that such a family together with a suitable object gives rise to a stratifying system; in particular, every stratifying system arises in this way. As an application, we present a stratifying system of infinite size that cannot be indexed by $(\mathbb{N}, \leq)$, where $\leq$ is the natural order.

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Edson Ribeiro Alvares, Matheus Vinicius dos Santos. 2026-07-27. Stratifying Systems via a Nested Family of Torsion Pairs. https://doi.org/10.4171/rmi%2F1625

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