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The Tambara-Yamagami calculus and finite semigroups

  • Super Cao
  • Daniel Tubbenhauer
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Abstract

Tambara-Yamagami categories are among the simplest fusion categories beyond the pointed case: one adds a single noninvertible simple object to a finite group of invertible ones. We ask what remains of their (diagrammatic) calculus when the group is replaced by a finite semigroup, and develop the resulting (diagrammatic) calculus.

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Cite

BibTeXRIS
BibTeX
@misc{cao2026tambarayamagami,
  title = {{The Tambara-Yamagami calculus and finite semigroups}},
  author = {Super Cao and Daniel Tubbenhauer},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.28957},
  eprint = {2609.28957},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.28957},
}
RIS
TY  - UNPB
TI  - The Tambara-Yamagami calculus and finite semigroups
AU  - Super Cao
AU  - Daniel Tubbenhauer
PY  - 2026
DA  - 2026/09/24
PB  - arXiv
DO  - 10.48550/arxiv.2609.28957
UR  - https://arxiv.org/abs/2609.28957
AB  - Tambara-Yamagami categories are among the simplest fusion categories beyond the pointed case: one adds a single noninvertible simple object to a finite group of invertible ones. We ask what remains of their (diagrammatic) calculus when the group is replaced by a finite semigroup, and develop the resulting (diagrammatic) calculus.
ER  -