Reflexive dg categories in algebra and topology
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908705184808960 |
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| author | Booth, Matt Goodbody, Isambard Opper, Sebastian |
| author_facet | Booth, Matt Goodbody, Isambard Opper, Sebastian |
| contents | Reflexive dg categories were introduced by Kuznetsov and Shinder to abstract the duality between bounded and perfect derived categories. In particular this duality relates their Hochschild cohomologies, autoequivalence groups, and semiorthogonal decompositions. We establish reflexivity in a variety of settings including affine schemes, simple-minded collections, chain and cochain dg algebras of topological spaces, Ginzburg dg algebras, and Fukaya categories of cotangent bundles and surfaces as well as the closely related class of graded gentle algebras. Our proofs are based on the interplay of reflexivity with gluings, derived completions, and Koszul duality. In particular we show that for certain (co)connective dg algebras, reflexivity is equivalent to derived completeness. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_11213 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Reflexive dg categories in algebra and topology Booth, Matt Goodbody, Isambard Opper, Sebastian Representation Theory Algebraic Geometry Algebraic Topology Category Theory Symplectic Geometry 18G35, 16E45, 18G80, 14A30, 13D09, 55U30 Reflexive dg categories were introduced by Kuznetsov and Shinder to abstract the duality between bounded and perfect derived categories. In particular this duality relates their Hochschild cohomologies, autoequivalence groups, and semiorthogonal decompositions. We establish reflexivity in a variety of settings including affine schemes, simple-minded collections, chain and cochain dg algebras of topological spaces, Ginzburg dg algebras, and Fukaya categories of cotangent bundles and surfaces as well as the closely related class of graded gentle algebras. Our proofs are based on the interplay of reflexivity with gluings, derived completions, and Koszul duality. In particular we show that for certain (co)connective dg algebras, reflexivity is equivalent to derived completeness. |
| title | Reflexive dg categories in algebra and topology |
| topic | Representation Theory Algebraic Geometry Algebraic Topology Category Theory Symplectic Geometry 18G35, 16E45, 18G80, 14A30, 13D09, 55U30 |
| url | https://arxiv.org/abs/2506.11213 |