Bibliographic Information: D´ecoppet, T.D. (2024). Extension Theory and Fermionic Strongly Fusion 2-Categories (with an Appendix by Thibault Didier D'ecoppet and Theo Johnson-Freyd). Symmetry, Integrability and Geometry: Methods and Applications, 20(2024), 092, 20 pages. https://doi.org/10.3842/SIGMA.2024.092
Research Objective: This paper aims to classify fermionic strongly fusion 2-categories, motivated by their role in the broader classification of topological orders in (3+1) dimensions.
Methodology: The paper utilizes the framework of group graded extension theory for fusion 2-categories. It leverages the existence of the relative 2-Deligne tensor product and analyzes the Brauer–Picard space associated with the fusion 2-category 2SVect.
Key Findings:
Main Conclusions: The paper provides a comprehensive classification of fermionic strongly fusion 2-categories, building upon previous work on bosonic strongly fusion 2-categories and invertible fusion 2-categories.
Significance: This research contributes significantly to the understanding of fusion 2-categories, particularly in the context of topological quantum field theories and the classification of topological orders.
Limitations and Future Research: The paper primarily focuses on fermionic strongly fusion 2-categories with a faithful grading. Further research could explore the classification of such categories without this restriction or investigate the connection with Tambara–Yamagami 2-categories in the context of extension theory.
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