Twin TQFTs and Frobenius algebras

Carmen Caprau

doi:10.1155/2013/407068

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arXiv · 0901.2979

Twin TQFTs and Frobenius algebras

Carmen Caprau

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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.

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Carmen Caprau. 2011-07-27. Twin TQFTs and Frobenius algebras. https://doi.org/10.1155/2013%2F407068

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