t-structures are normal torsion theories

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.

Minor typographical corrections from v1; 25 pages; to appear in "Applied Categorical Structures"

References in corpus (4)

• Higher Topos Theory
• Differential cohomology in a cohesive infinity-topos
• The unification of Mathematics via Topos Theory
• Hearts and towers in stable infinity-categories

Cited by in corpus (6)

• Enhancing the filtered derived category
• Model $\infty$-categories I: some pleasant properties of the $\infty$-category of simplicial spaces
• Hearts and towers in stable infinity-categories
• Localization theory for derivators
• Recollements in stable $\infty$-categories
• A standard theorem on adjunctions in two variables