00906nas a2200157 4500008004100000022001400041245004500055210004400100260000800144300001400152490000700166520048600173100002300659700002000682856004600702 2016 eng d a1572-909500at-Structures are Normal Torsion Theories0 atStructures are Normal Torsion Theories cApr a181–2080 v243 a
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.
1 aFiorenza, Domenico1 aLoregian, Fosco uhttps://doi.org/10.1007/s10485-015-9393-z