t-structures on stable infinity-categories

TL;DR

This paper redefines the classical theory of t-structures within stable infinity-categories using reflective factorization systems, enabling new insights into their properties and applications in modern homotopical and algebraic contexts.

Contribution

It translates classical t-structure theory into the infinity-categorical setting via factorization systems, opening pathways for advanced applications like Postnikov towers and stability conditions.

Findings

Reformulation of t-structures using reflective factorization systems

Development of a framework connecting t-structures with Postnikov towers

Application to the study of Bridgeland's stability conditions

Abstract

The present work re-enacts the classical theory of t-structures reducing the classical definition given in *Faisceaux Pervers* to a rather primitive categorical gadget: suitable reflective factorization systems. This translation is only possible due to the virtues of the infinity-categorical setting. Once the basic theory of t-structure has been developed, a natural direction of research is to develop a comprehensive treatment of t-structure in the "torsio-centric" perspective: we apply the technology of factorization systems to the theory of Postnikov towers, to the proof of the abelianity of the heart of a t-structure, and to the theory of Bridgeland's stability conditions.