t-structures are normal torsion theories

TL;DR

This paper establishes a correspondence between t-structures in stable ∞-categories and normal torsion theories, providing a new characterization via quasicategorical factorization systems.

Contribution

It introduces a novel equivalence between t-structures and normal torsion theories in stable ∞-categories, expanding the understanding of their structural properties.

Findings

t-structures are characterized as normal torsion theories

equivalence between t-structures and factorization systems with specific properties

provides a new framework for analyzing stable ∞-categories

Abstract

We characterize $t$-structures in stable $\infty$-categories as suitable quasicategorical factorization systems. More precisely we show that a $t$-structure $\mathfrak{t}$ on a stable $\infty$-category $\mathbf{C}$ is equivalent to a normal torsion theory $\mathbb{F}$ on $\mathbf{C}$, i.e. to a factorization system $\mathbb{F}=(\mathcal{E},\mathcal{M})$ where both classes satisfy the 3-for-2 cancellation property, and a certain compatibility with pullbacks/pushouts.