Differential Calculus of Hochschild Pairs for Infinity-Categories
In this paper, we provide a conceptual new construction of the algebraic structure on the pair of the Hochschild cohomology spectrum (cochain complex) and Hochschild homology spectrum, which is analogous to the structure of calculus on a manifold. This algebraic structure is encoded by a two-colored...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2020 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2020
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/211023 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Differential Calculus of Hochschild Pairs for Infinity-Categories. Isamu Iwanari. SIGMA 16 (2020), 097, 57 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862734000167059456 |
|---|---|
| author | Iwanari, Isamu |
| author_facet | Iwanari, Isamu |
| citation_txt | Differential Calculus of Hochschild Pairs for Infinity-Categories. Isamu Iwanari. SIGMA 16 (2020), 097, 57 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | In this paper, we provide a conceptual new construction of the algebraic structure on the pair of the Hochschild cohomology spectrum (cochain complex) and Hochschild homology spectrum, which is analogous to the structure of calculus on a manifold. This algebraic structure is encoded by a two-colored operad introduced by Kontsevich and Soibelman. We prove that for a stable idempotent-complete infinity-category, the pair of its Hochschild cohomology and homology spectra naturally admits the structure of an algebra over the operad. Moreover, we prove a generalization to the equivariant context.
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| first_indexed | 2026-04-17T15:59:34Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211023 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-04-17T15:59:34Z |
| publishDate | 2020 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Iwanari, Isamu 2025-12-22T09:31:36Z 2020 Differential Calculus of Hochschild Pairs for Infinity-Categories. Isamu Iwanari. SIGMA 16 (2020), 097, 57 pages 1815-0659 2020 Mathematics Subject Classification: 16E40; 18N60; 18M60 arXiv:1904.02359 https://nasplib.isofts.kiev.ua/handle/123456789/211023 https://doi.org/10.3842/SIGMA.2020.097 In this paper, we provide a conceptual new construction of the algebraic structure on the pair of the Hochschild cohomology spectrum (cochain complex) and Hochschild homology spectrum, which is analogous to the structure of calculus on a manifold. This algebraic structure is encoded by a two-colored operad introduced by Kontsevich and Soibelman. We prove that for a stable idempotent-complete infinity-category, the pair of its Hochschild cohomology and homology spectra naturally admits the structure of an algebra over the operad. Moreover, we prove a generalization to the equivariant context. The author would like to thank Takuo Matsuoka for valuable and inspiring conversations related to the subject of this paper. He would like to thank everyone who provided constructive feedback at his talks about the main content of this paper. He would also like to thank the referees for their useful suggestions. This work is supported by JSPS KAKENHI grant 17K14150. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Differential Calculus of Hochschild Pairs for Infinity-Categories Article published earlier |
| spellingShingle | Differential Calculus of Hochschild Pairs for Infinity-Categories Iwanari, Isamu |
| title | Differential Calculus of Hochschild Pairs for Infinity-Categories |
| title_full | Differential Calculus of Hochschild Pairs for Infinity-Categories |
| title_fullStr | Differential Calculus of Hochschild Pairs for Infinity-Categories |
| title_full_unstemmed | Differential Calculus of Hochschild Pairs for Infinity-Categories |
| title_short | Differential Calculus of Hochschild Pairs for Infinity-Categories |
| title_sort | differential calculus of hochschild pairs for infinity-categories |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211023 |
| work_keys_str_mv | AT iwanariisamu differentialcalculusofhochschildpairsforinfinitycategories |