Model theory in compactly generated (tensor-)triangulated categories
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913334723346432 |
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| author | Prest, Mike Wagstaffe, Rose |
| author_facet | Prest, Mike Wagstaffe, Rose |
| contents | We give an account of model theory in the context of compactly generated triangulated and tensor-triangulated categories ${\cal T}$. We describe pp formulas, pp-types and free realisations in such categories and we prove elimination of quantifiers and elimination of imaginaries. We compare the ways in which definable subcategories of ${\cal T}$ may be specified. Then we link definable subcategories of ${\cal T}$ and finite-type torsion theories on the category of modules over the compact objects of ${\cal T}$. We briefly consider spectra and dualities. If ${\cal T}$ is tensor-triangulated then new features appear, in particular there is an internal duality in rigidly-compactly generated tensor-triangulated categories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_10629 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Model theory in compactly generated (tensor-)triangulated categories Prest, Mike Wagstaffe, Rose Representation Theory Category Theory Logic 18G80, 18E45, 03C60 We give an account of model theory in the context of compactly generated triangulated and tensor-triangulated categories ${\cal T}$. We describe pp formulas, pp-types and free realisations in such categories and we prove elimination of quantifiers and elimination of imaginaries. We compare the ways in which definable subcategories of ${\cal T}$ may be specified. Then we link definable subcategories of ${\cal T}$ and finite-type torsion theories on the category of modules over the compact objects of ${\cal T}$. We briefly consider spectra and dualities. If ${\cal T}$ is tensor-triangulated then new features appear, in particular there is an internal duality in rigidly-compactly generated tensor-triangulated categories. |
| title | Model theory in compactly generated (tensor-)triangulated categories |
| topic | Representation Theory Category Theory Logic 18G80, 18E45, 03C60 |
| url | https://arxiv.org/abs/2304.10629 |