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 , 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.

Abstract licence: CC BY

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