Hearts and towers in stable infinity-categories

We exploit the equivalence between t-structures and normal torsion theories on stable infinity-categories to unify two apparently separated constructions in the theory of triangulated categories: the characterization of bounded t-structures in terms of their hearts and semiorthogonal decompositions on triangulated categories. In the stable infinity-categorical context both notions stem from a single construction, the Postnikov tower of a morphism induced by a $\mathbb{Z}$-equivariant multiple (bireflective and normal) factorization system $\{\mathbb{F}_i\}_{i\in J}$. For J = $\mathbb{Z}$ with its obvious self-action, we recover the notion of Postnikov towers in a triangulated category endowed with a t-structure, and give a proof of the the abelianity of the heart in the infinity-stable setting. For J is a finite totally ordered set, we recover the theory of semiorthogonal decompositions.