Twin TQFTs and Frobenius Algebras

Carmen Caprau

Journal of Mathematics, 2013, vol. 2013, 1-25

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 consists of a commutative Frobenius algebra , a symmetric Frobenius algebra , and an algebra homomorphism with dual , 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.

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:407068

DOI: 10.1155/2013/407068

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