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arXiv · 2307.05309

Symmetric monoidal equivalences of topological quantum field theories in dimension two and Frobenius algebras

Pablo S. Ocal
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Abstract

We show that the canonical equivalences of categories between 2-dimensional (unoriented) topological quantum field theories valued in a symmetric monoidal category and (extended) commutative Frobenius algebras in that symmetric monoidal category are symmetric monoidal equivalences. As an application, we recover that the invariant of 2-dimensional manifolds given by the product of (extended) commutative Frobenius algebras in a symmetric tensor category is the multiplication of the invariants given by each of the algebras.

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Pablo S. Ocal. 2023-07-11. Symmetric monoidal equivalences of topological quantum field theories in dimension two and Frobenius algebras. https://doi.org/10.1090/proc%2F16719

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