Twin TQFTs and Frobenius Algebras
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...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2013-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/407068 |
| Summary: | 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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| ISSN: | 2314-4629 2314-4785 |