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

Fuente: arXiv
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Main Author: Ocal, Pablo S.
Format: Preprint
Published: 2023
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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