Frobenius Algebras and Dual Bimodules in Monoidal 2-Categories
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866916074137583616 |
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| author | Xu, Hao |
| author_facet | Xu, Hao |
| contents | We explicitly construct dual bimodules in a semistrict monoidal 2-category, using Frobenius algebra structure. The main result shows that a coherent dual of the underlying object can be promoted to a coherent dual of the bimodule, with zigzag 2-isomorphisms additionally require special Frobenius structures. We also prove that every special Frobenius algebra in $\mathbf{2Vect}$ is rigid, via a categorified Casimir object argument, and discuss the relationship between the Frobenius, rigid, special Frobenius, and separable algebra hierarchies. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2606_02046 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Frobenius Algebras and Dual Bimodules in Monoidal 2-Categories Xu, Hao Quantum Algebra Category Theory 18M25 (Primary) 18N05 18M30 (Secondary) We explicitly construct dual bimodules in a semistrict monoidal 2-category, using Frobenius algebra structure. The main result shows that a coherent dual of the underlying object can be promoted to a coherent dual of the bimodule, with zigzag 2-isomorphisms additionally require special Frobenius structures. We also prove that every special Frobenius algebra in $\mathbf{2Vect}$ is rigid, via a categorified Casimir object argument, and discuss the relationship between the Frobenius, rigid, special Frobenius, and separable algebra hierarchies. |
| title | Frobenius Algebras and Dual Bimodules in Monoidal 2-Categories |
| topic | Quantum Algebra Category Theory 18M25 (Primary) 18N05 18M30 (Secondary) |
| url | https://arxiv.org/abs/2606.02046 |