Deformations of triangulated categories with t-structures via derived injectives
Abstract
This paper provides the final ingredient in the development of the deformation theory of pretriangulated dg-categories endowed with a nice t-structure, which was initiated by the authors and is modeled after the previously developed deformation theory of abelian categories. We show how to extend a t-structure on a pretriangulated dg-category to its dg-derived category so that the Yoneda embedding becomes t-exact. We construct several equivalences between deformation problems; in particular, we prove a deformation equivalence between the bounded t-deformations of a bounded t-dg-category on the one hand, and dg-deformations of the dg-category of derived injective ind-dg-objects on the other hand. Since this latter dg-category is cohomologically concentrated in nonpositive degrees, we do not encounter curvature.
Cite
@article{arxiv.2411.15359,
title = {Deformations of triangulated categories with t-structures via derived injectives},
author = {Francesco Genovese and Wendy Lowen and Julie Symons and Michel Van den Bergh},
journal= {arXiv preprint arXiv:2411.15359},
year = {2024}
}