Deformations of triangulated categories with t-structures via derived injectives
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866913583874441216 |
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| author | Genovese, Francesco Lowen, Wendy Symons, Julie Bergh, Michel Van den |
| author_facet | Genovese, Francesco Lowen, Wendy Symons, Julie Bergh, Michel Van den |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_15359 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Deformations of triangulated categories with t-structures via derived injectives Genovese, Francesco Lowen, Wendy Symons, Julie Bergh, Michel Van den Category Theory K-Theory and Homology 18G80 (Primary), 16E45, 13D10, 18G25 (Secondary) 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. |
| title | Deformations of triangulated categories with t-structures via derived injectives |
| topic | Category Theory K-Theory and Homology 18G80 (Primary), 16E45, 13D10, 18G25 (Secondary) |
| url | https://arxiv.org/abs/2411.15359 |