Symmetric monoidal equivalences of topological quantum field theories in dimension two and Frobenius algebras
Copyright policy )Symmetric monoidal equivalences of topological quantum field theories in dimension two and Frobenius algebras
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.
topological quantum field theory, Topological quantum field theories (aspects of differential topology), symmetric monoidal equivalence, Braided monoidal categories and ribbon categories, Finite-type and quantum invariants, topological quantum field theories (TQFT), Frobenius algebra, Mathematics - Quantum Algebra, 57R56, 18M05, 57K16, 18M15, 16L60, FOS: Mathematics, Monoidal categories, symmetric monoidal categories, Quantum Algebra (math.QA), Quasi-Frobenius rings
topological quantum field theory, Topological quantum field theories (aspects of differential topology), symmetric monoidal equivalence, Braided monoidal categories and ribbon categories, Finite-type and quantum invariants, topological quantum field theories (TQFT), Frobenius algebra, Mathematics - Quantum Algebra, 57R56, 18M05, 57K16, 18M15, 16L60, FOS: Mathematics, Monoidal categories, symmetric monoidal categories, Quantum Algebra (math.QA), Quasi-Frobenius rings
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