T-Structures as Classifying Objects for Exact Structures on Triangulated Categories Article Swipe
Revista, Zen
,
MATH, 10
·
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.5281/zenodo.17830351
YOU?
·
· 2025
· Open Access
·
· 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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- https://doi.org/10.5281/zenodo.17830351
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- green
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All OpenAlex metadata
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https://openalex.org/W7109165865Canonical identifier for this work in OpenAlex
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T-Structures as Classifying Objects for Exact Structures on Triangulated CategoriesWork title
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articleOpenAlex work type
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2025Year of publication
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2025-12-05Full publication date if available
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Revista, Zen, MATH, 10List of authors in order
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https://doi.org/10.5281/zenodo.17830351Publisher landing page
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YesWhether a free full text is available
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greenOpen access status per OpenAlex
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https://doi.org/10.5281/zenodo.17830351Direct OA link when available
- Concepts
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Triangulated category, Representation (politics), Mathematics, Triangulation, Computer science, Algebraic structure, Algebra over a field, Theoretical computer science, Data structure, Homological algebra, Algebraic number, Object (grammar), Artificial intelligenceTop concepts (fields/topics) attached by OpenAlex
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0Total citation count in OpenAlex
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