Extension Theory and Fermionic Strongly Fusion 2-Categories (with an Appendix by Thibault Didier Décoppet and Theo Johnson-Freyd)
We study group-graded extensions of fusion 2-categories. As an application, we obtain a homotopy theoretic classification of fermionic strongly fusion 2-categories. We examine various examples in detail.
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2024 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2024
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/212614 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Extension Theory and Fermionic Strongly Fusion 2-Categories (with an Appendix by Thibault Didier Décoppet and Theo Johnson-Freyd). Thibault Didier Décoppet. SIGMA 20 (2024), 092, 20 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862705091877797888 |
|---|---|
| author | Décoppet, Thibault Didier |
| author_facet | Décoppet, Thibault Didier |
| citation_txt | Extension Theory and Fermionic Strongly Fusion 2-Categories (with an Appendix by Thibault Didier Décoppet and Theo Johnson-Freyd). Thibault Didier Décoppet. SIGMA 20 (2024), 092, 20 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We study group-graded extensions of fusion 2-categories. As an application, we obtain a homotopy theoretic classification of fermionic strongly fusion 2-categories. We examine various examples in detail.
|
| first_indexed | 2026-03-18T20:47:57Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212614 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-18T20:47:57Z |
| publishDate | 2024 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Décoppet, Thibault Didier 2026-02-09T08:06:41Z 2024 Extension Theory and Fermionic Strongly Fusion 2-Categories (with an Appendix by Thibault Didier Décoppet and Theo Johnson-Freyd). Thibault Didier Décoppet. SIGMA 20 (2024), 092, 20 pages 1815-0659 2020 Mathematics Subject Classification: 18M20; 18N25 arXiv:2403.03211 https://nasplib.isofts.kiev.ua/handle/123456789/212614 https://doi.org/10.3842/SIGMA.2024.092 We study group-graded extensions of fusion 2-categories. As an application, we obtain a homotopy theoretic classification of fermionic strongly fusion 2-categories. We examine various examples in detail. I am particularly indebted to Theo Johnson-Freyd and David Reutter for sharing some of the ideas of their proof of the completely general version of group-graded extension theory, which have inspired our proof of Theorem 3.11, and to Matthew Yu for help with the cohomology computations of Section 4. I would also like to thank the referees for suggesting many invaluable improvements and clarifications. This work was supported in part by the Simons Collaboration on Global Categorical Symmetries. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Extension Theory and Fermionic Strongly Fusion 2-Categories (with an Appendix by Thibault Didier Décoppet and Theo Johnson-Freyd) Article published earlier |
| spellingShingle | Extension Theory and Fermionic Strongly Fusion 2-Categories (with an Appendix by Thibault Didier Décoppet and Theo Johnson-Freyd) Décoppet, Thibault Didier |
| title | Extension Theory and Fermionic Strongly Fusion 2-Categories (with an Appendix by Thibault Didier Décoppet and Theo Johnson-Freyd) |
| title_full | Extension Theory and Fermionic Strongly Fusion 2-Categories (with an Appendix by Thibault Didier Décoppet and Theo Johnson-Freyd) |
| title_fullStr | Extension Theory and Fermionic Strongly Fusion 2-Categories (with an Appendix by Thibault Didier Décoppet and Theo Johnson-Freyd) |
| title_full_unstemmed | Extension Theory and Fermionic Strongly Fusion 2-Categories (with an Appendix by Thibault Didier Décoppet and Theo Johnson-Freyd) |
| title_short | Extension Theory and Fermionic Strongly Fusion 2-Categories (with an Appendix by Thibault Didier Décoppet and Theo Johnson-Freyd) |
| title_sort | extension theory and fermionic strongly fusion 2-categories (with an appendix by thibault didier décoppet and theo johnson-freyd) |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212614 |
| work_keys_str_mv | AT decoppetthibaultdidier extensiontheoryandfermionicstronglyfusion2categorieswithanappendixbythibaultdidierdecoppetandtheojohnsonfreyd |