Symmetric monoidal equivalences of topological quantum field theories in dimension two and Frobenius algebras
arXiv:2307.05309 · doi:10.1090/proc/16719
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.
4 pages, added acknowledgments, added referee corrections, to appear in Proc. Amer. Math. Soc