2024/11/22 by Francesco Genovese, Genovese, Francesco, Wendy Lowen +5
Mathematics · #13D10 #16E45 #18G25 (Secondary) #18G80 (Primary) #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)
paper · pdf · doi:10.48550/arxiv.2411.15359
openalex publication_date 2024/11/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
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.