Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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.

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The categories of this paper are: cond-mat
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The categories of this paper are: q-fin
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-th
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The categories of this paper are: quant-ph
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The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
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The categories of this paper are: funct-an
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The categories of this paper are: cs
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The categories of this paper are: econ
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The categories of this paper are: nucl-ex