Stratifying Systems via a Nested Family of Torsion Pairs

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 $(\mathbb{N},\le )$, where $\le$ is the natural order.

arXiv comment34 pages. This is the author's accepted manuscript of the article, Edson Ribeiro Alvares and Matheus Vinicius dos Santos, "Stratifying Systems via a Nested Family of Torsion Pairs'', Revista Matemática Iberoamericana, textbf{42} (2026), no.~4, 1201--1226. The final Version of Record is available at https://doi.org/10.4171/RMI/1625