Mathematics

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