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

Ocal, Pablo

doi:10.1090/proc/16719

Symmetric monoidal equivalences of topological quantum field theories in dimension two and Frobenius algebras
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by Pablo S. Ocal;

Proc. Amer. Math. Soc. 152 (2024), 2261-2265

DOI: https://doi.org/10.1090/proc/16719

Published electronically: March 14, 2024

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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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