With braiding
With duals for objects
category with duals (list of them)
dualizable object (what they have)
ribbon category, a.k.a. tortile category
With duals for morphisms
monoidal dagger-category?
With traces
Closed structure
Special sorts of products
Semisimplicity
Morphisms
Internal monoids
Examples
Theorems
In higher category theory
algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)
quantum mechanical system, quantum probability
interacting field quantization
Super-modular tensor categories are to modular tensor categories as spin Chern-Simons theory is to Chern-Simons theory. Concretely, these are pre-modular tensor categories whose Müger center? is equivalent as a symmetric monoidal category to that of super vector spaces.
Paul Bruillard, Cesar Galindo, Tobias Hagge, Siu-Hung Ng, Julia Yael Plavnik, Eric C. Rowell, Zhenghan Wang: Fermionic Modular Categories and the 16-fold Way, J. Math. Phys. 58 (2017) 041704 [doi:10.1063/1.4982048, arXiv:1603.09294]
Parsa Bonderson, Eric C. Rowell, Qing Zhang, Zhenghan Wang: Congruence Subgroups and Super-Modular Categories, Pacific J. Math. 296 (2018) 257-270 [arXiv:1704.02041, doi:10.2140/pjm.2018.296.257]
Qing Zhang: Super-Modular Categories, PhD thesis, Texas A&M University (2019) [pdf, pdf]
Jin-Beom Bae et al.: Fermionic rational conformal field theories and modular linear differential equations, Progress of Theoretical and Experimental Physics 2021 8 (2021) 08B104 [doi:10.1093/ptep/ptab033, arXiv:2010.12392]
Created on March 30, 2025 at 08:29:44. See the history of this page for a list of all contributions to it.