T-Structures as Classifying Objects for Exact Structures on Triangulated Categories Article Swipe
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· 2025
· Open Access
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· DOI: https://doi.org/10.5281/zenodo.17830351
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-structures, providing tools for understanding the relationships between various homological structures on triangulated categories. This study has implications for representation theory, algebraic geometry, and the homological study of singularities, providing new insights and paving the way for further research into the interplay between triangulated and exact categories.
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- Type
- article
- Landing Page
- https://doi.org/10.5281/zenodo.17830351
- OA Status
- green
- OpenAlex ID
- https://openalex.org/W7109165865