Zenodo (CERN European Organization for Nuclear Research)
T-Structures as Classifying Objects for Exact Structures on Triangulated Categories
2025
This paper investigates the role of t-structures as classifying objects for exact structures on triangulated categories. We demonstrate that the heart of a t-structure, under suitable conditions, can be equipped with an exact structure that is uniquely determined by the t-structure. Furthermore, we explore the converse, examining when a given exact structure on a triangulated category can be realized as the heart of a t-structure. We introduce a novel framework for comparing different exact structures via t-struct…