Article · Wikipedia archive · Last revised Jun 19, 2026

Spherical category

In category theory, a branch of mathematics, a spherical category is a pivotal category in which left and right traces coincide. Spherical fusion categories give rise to a family of three-dimensional topological state sum models, the Turaev-Viro model, or rather Turaev-Viro-Barrett-Westbury model.

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Jun 19, 2026
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In category theory, a branch of mathematics, a spherical category is a pivotal category (a monoidal category with traces) in which left and right traces coincide.1 Spherical fusion categories give rise to a family of three-dimensional topological state sum models (a particular formulation of a topological quantum field theory2), the Turaev-Viro model, or rather Turaev-Viro-Barrett-Westbury model.3

References

References

  1. John W. Barrett; Bruce W. Westbury (1999). "Spherical Categories". Advances in Mathematics. 143 (2): 357–375. arXiv:hep-th/9310164. doi:10.1006/aima.1998.1800.
  2. Turaev, Vladimir Georgievič; Virelizier, Alexis (2017). Monoidal categories and topological field theory. Progress in mathematics. Cham: Birkhäuser Springer international publishing. ISBN 978-3-319-49833-1.
  3. "Turaev-Viro model". nLab. Retrieved 7 August 2017.