Twin TQFTs and Frobenius algebras
Abstract
We introduce the category of singular 2-dimensional cobordisms and show that it admits a completely algebraic description as the free symmetric monoidal category on a twin Frobenius algebra, by providing a description of this category in terms of generators and relations. A twin Frobenius algebra (C, W, z, z^*) consists of a commutative Frobenius algebra C, a symmetric Frobenius algebra W, and an algebra homomorphism z: C - > W with dual z^*: W -> C, satisfying some extra conditions. We also introduce a generalized 2-dimensional Topological Quantum Field Theory defined on singular 2-dimensional cobordisms and show that it is equivalent to a twin Frobenius algebra in a symmetric monoidal category.
Keywords
Cite
@article{arxiv.0901.2979,
title = {Twin TQFTs and Frobenius algebras},
author = {Carmen Caprau},
journal= {arXiv preprint arXiv:0901.2979},
year = {2015}
}
Comments
38 pages, many figures; some concepts have been clarified; references and proofs have been added