Formality and strongly unique enhancements
Antonio Lorenzin
TL;DR
This paper establishes a necessary and sufficient condition for the strong uniqueness of DG-enhancements in triangulated categories, generalizing to any commutative ring and providing new examples and results on derived categories.
Contribution
It introduces a criterion for strong uniqueness of DG-enhancements applicable over any commutative ring, expanding the understanding of triangulated categories.
Findings
Provided a necessary and sufficient condition for strong uniqueness.
Generalized the approach to linearity over any commutative ring.
Showed the bounded derived category of an exact category has a unique enhancement.
Abstract
Inspired by the intrinsic formality of graded algebras, we prove a necessary and sufficient condition for strongly uniqueness of DG-enhancements. This approach offers a generalization to linearity over any commutative ring. In particular, we obtain several new examples of triangulated categories with a strongly unique DG-enhancement. Moreover, we also show that the bounded derived category of an exact category has a unique enhancement.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Rings, Modules, and Algebras