Formality and strongly unique enhancements
arXiv:2204.09527 · doi:10.1016/j.jalgebra.2025.01.002
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.
32 pages. Improved exposition based on referees' insights