Stratifying Systems via a Nested Family of Torsion Pairs

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.