On extended Frobenius structures
Quantum Algebra
2025-11-04 v2
Abstract
A classical result in quantum topology is that oriented 2-dimensional topological quantum field theories (2-TQFTs) are fully classified by commutative Frobenius algebras. In 2006, Turaev and Turner introduced additional structure on Frobenius algebras, forming what are called extended Frobenius algebras, to classify 2-TQFTs in the unoriented case. This work provides a systematic study of extended Frobenius algebras in various settings: over a field, in a monoidal category, and in the framework of monoidal functors. Numerous examples, classification results, and general constructions of extended Frobenius algebras are established.
Cite
@article{arxiv.2410.18232,
title = {On extended Frobenius structures},
author = {Agustina Czenky and Jacob Kesten and Abiel Quinonez and Chelsea Walton},
journal= {arXiv preprint arXiv:2410.18232},
year = {2025}
}
Comments
v2. 22 pages + appendices. To appear in Theory and Applications of Categories