Symmetric monoidal equivalences of topological quantum field theories in dimension two and Frobenius algebras
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914828558270464 |
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| author | Ocal, Pablo S. |
| author_facet | Ocal, Pablo S. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_05309 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Symmetric monoidal equivalences of topological quantum field theories in dimension two and Frobenius algebras Ocal, Pablo S. Quantum Algebra 57R56, 18M05, 57K16, 18M15, 16L60 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. |
| title | Symmetric monoidal equivalences of topological quantum field theories in dimension two and Frobenius algebras |
| topic | Quantum Algebra 57R56, 18M05, 57K16, 18M15, 16L60 |
| url | https://arxiv.org/abs/2307.05309 |