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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.07969 |
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| _version_ | 1866908584385708032 |
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| author | Shibata, Taiki Shimizu, Kenichi |
| author_facet | Shibata, Taiki Shimizu, Kenichi |
| contents | For coalgebras $C$ and $D$, Takeuchi proved that the category of linear functors from $\mathfrak{M}^C$ to $\mathfrak{M}^D$ preserving small coproducts is equivalent to the category of $C$-$D$-bicomodules, where $\mathfrak{M}^C$ for a coalgebra $C$ means the category of right $C$-comodules. We formulate and prove an equivariant version of this result for module coalgebras over a bialgebra. As an application, for a bialgebra $H$, we establish an equivalence of the 2-category of a particular class of module categories over the monoidal category $\mathfrak{M}^H$ and the 2-category of a particular class of module categories over the monoidal category ${}_H\mathfrak{M}$ of left $H$-modules. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_07969 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Equivariant Eilenberg-Watts theorem for module coalgebras Shibata, Taiki Shimizu, Kenichi Quantum Algebra Rings and Algebras 18M05, 16T05 For coalgebras $C$ and $D$, Takeuchi proved that the category of linear functors from $\mathfrak{M}^C$ to $\mathfrak{M}^D$ preserving small coproducts is equivalent to the category of $C$-$D$-bicomodules, where $\mathfrak{M}^C$ for a coalgebra $C$ means the category of right $C$-comodules. We formulate and prove an equivariant version of this result for module coalgebras over a bialgebra. As an application, for a bialgebra $H$, we establish an equivalence of the 2-category of a particular class of module categories over the monoidal category $\mathfrak{M}^H$ and the 2-category of a particular class of module categories over the monoidal category ${}_H\mathfrak{M}$ of left $H$-modules. |
| title | Equivariant Eilenberg-Watts theorem for module coalgebras |
| topic | Quantum Algebra Rings and Algebras 18M05, 16T05 |
| url | https://arxiv.org/abs/2510.07969 |