Tensor extriangulated categories
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909510624346112 |
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| author | Bennett-Tennenhaus, Raphael Goodbody, Isambard Letz, Janina C. Shah, Amit |
| author_facet | Bennett-Tennenhaus, Raphael Goodbody, Isambard Letz, Janina C. Shah, Amit |
| contents | A tensor extriangulated category is an extriangulated category with a symmetric monoidal structure that is compatible with the extriangulated structure. To this end we define a notion of a biextriangulated functor $\mathcal{A} \times \mathcal{B} \to \mathcal{C}$, with compatibility conditions between the components. We have two versions of compatibility conditions, the stronger depending on the higher extensions of the extriangulated categories. We give many examples of tensor extriangulated categories. Finally, we generalise Balmer's classification of thick tensor ideals to tensor extriangulated categories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_18257 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tensor extriangulated categories Bennett-Tennenhaus, Raphael Goodbody, Isambard Letz, Janina C. Shah, Amit Category Theory 18M05 (Primary) 18E05, 18G80, 18A23, 18G99 (Secondary) A tensor extriangulated category is an extriangulated category with a symmetric monoidal structure that is compatible with the extriangulated structure. To this end we define a notion of a biextriangulated functor $\mathcal{A} \times \mathcal{B} \to \mathcal{C}$, with compatibility conditions between the components. We have two versions of compatibility conditions, the stronger depending on the higher extensions of the extriangulated categories. We give many examples of tensor extriangulated categories. Finally, we generalise Balmer's classification of thick tensor ideals to tensor extriangulated categories. |
| title | Tensor extriangulated categories |
| topic | Category Theory 18M05 (Primary) 18E05, 18G80, 18A23, 18G99 (Secondary) |
| url | https://arxiv.org/abs/2502.18257 |