Deligne-Knop tensor categories and functoriality
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929410244870144 |
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| author | Entova-Aizenbud, Inna Heidersdorf, Thorsten |
| author_facet | Entova-Aizenbud, Inna Heidersdorf, Thorsten |
| contents | A general construction of Knop creates a symmetric monoidal category $\mathcal{T}(\mathcal{A},δ)$ from any regular category $\mathcal{A}$ and a fixed degree function $δ$. A special case of this construction are the Deligne categories $\underline{\operatorname{Rep}}(S_t)$ and $\underline{\operatorname{Rep}}(GL_t(\mathbb{F}_q))$. We discuss when a functor $F:\mathcal{A} \to \mathcal{A}'$ between regular categories induces a symmetric monoidal functor $\mathcal{T}(\mathcal{A},δ) \to \mathcal{T}(\mathcal{A}',δ')$. We then give a criterion when a pair of adjoint functors between two regular categories $\mathcal{A}, \ \mathcal{A}'$ lifts to a pair of adjoint functors between $\mathcal{T}(\mathcal{A},δ)$ and $\mathcal{T}(\mathcal{A}',δ')$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_03798 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Deligne-Knop tensor categories and functoriality Entova-Aizenbud, Inna Heidersdorf, Thorsten Representation Theory Category Theory 05E05, 18D10, 20C30 A general construction of Knop creates a symmetric monoidal category $\mathcal{T}(\mathcal{A},δ)$ from any regular category $\mathcal{A}$ and a fixed degree function $δ$. A special case of this construction are the Deligne categories $\underline{\operatorname{Rep}}(S_t)$ and $\underline{\operatorname{Rep}}(GL_t(\mathbb{F}_q))$. We discuss when a functor $F:\mathcal{A} \to \mathcal{A}'$ between regular categories induces a symmetric monoidal functor $\mathcal{T}(\mathcal{A},δ) \to \mathcal{T}(\mathcal{A}',δ')$. We then give a criterion when a pair of adjoint functors between two regular categories $\mathcal{A}, \ \mathcal{A}'$ lifts to a pair of adjoint functors between $\mathcal{T}(\mathcal{A},δ)$ and $\mathcal{T}(\mathcal{A}',δ')$. |
| title | Deligne-Knop tensor categories and functoriality |
| topic | Representation Theory Category Theory 05E05, 18D10, 20C30 |
| url | https://arxiv.org/abs/2407.03798 |