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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2103.08686 |
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| _version_ | 1866911821185679360 |
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| author | Knop, Friedrich |
| author_facet | Knop, Friedrich |
| contents | To every regular category $\mathcal{A}$ equipped with a degree function $δ$ one can attach a pseudo-abelian tensor category $\mathcal{T}(\mathcal{A},δ)$. We show that the generating objects of $\mathcal{T}$ decompose canonically as a direct sum. In this paper we calculate morphisms, compositions of morphisms and tensor products of the summands. As a special case we recover the original construction of Deligne's category $\operatorname{Rep} S_t$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2103_08686 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | The subobject decomposition in enveloping tensor categories Knop, Friedrich Category Theory Representation Theory 18D10, 20F29, 08A62, 08B05 To every regular category $\mathcal{A}$ equipped with a degree function $δ$ one can attach a pseudo-abelian tensor category $\mathcal{T}(\mathcal{A},δ)$. We show that the generating objects of $\mathcal{T}$ decompose canonically as a direct sum. In this paper we calculate morphisms, compositions of morphisms and tensor products of the summands. As a special case we recover the original construction of Deligne's category $\operatorname{Rep} S_t$. |
| title | The subobject decomposition in enveloping tensor categories |
| topic | Category Theory Representation Theory 18D10, 20F29, 08A62, 08B05 |
| url | https://arxiv.org/abs/2103.08686 |