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-z01189nas a2200121 4500008004100000245005100041210004600092260001000138520072900148653011900877100002000996856005101016 2016 en d00at-structures on stable (infinity,1)-categories0 atstructures on stable infinity1categories bSISSA3 aThe present work re-enacts the classical theory of t-structures reducing the classical definition coming from Algebraic Geometry to a rather primitive categorical gadget: suitable reflective factorization systems (defined in the work of Rosický, Tholen, and Cassidy-Hébert-Kelly), which we call "normal torsion theories" following. A relation between these two objects has previously been noticed by other authors, on the level of the triangulated homotopy categories of stable (infinity,1)-categories. The main achievement of the present thesis is to observe and prove that this relation exists genuinely when the definition is lifted to the higher-dimensional world where the notion of triangulated category comes from.10acategory theory, higher category theory, factorization system, torsion theory, homological algebra, higher algebra1 aLoregian, Fosco uhttp://urania.sissa.it/xmlui/handle/1963/35202