TL;DR
This paper establishes precise conditions for when finite triangulated categories can be enhanced and proves that such enhancements are unique up to Morita equivalence, clarifying their structural properties.
Contribution
It provides a necessary and sufficient criterion for the existence of enhancements and demonstrates their uniqueness up to Morita equivalence in finite triangulated categories.
Findings
Criteria for enhancement existence
Uniqueness of enhancements up to Morita equivalence
Clarification of structural properties of finite triangulated categories
Abstract
We give a necessary and sufficient condition for the existence of an enhancement of a finite triangulated category. Moreover, we show that enhancements are unique when they exist, up to Morita equivalence.
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