Morita theory for quantales
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866916617993060352 |
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| author | Mesablishvili, Bachuki |
| author_facet | Mesablishvili, Bachuki |
| contents | Morita theory for quantales is developed. The main result of the paper is a characterization of those quantaloids (categories enriched in the symmetric monoidal closed category of sup-lattices) that are equivalent to modular categories over quantales. Based on this characterization, necessary and sufficient conditions are derived for two quantales to be Morita-equivalent, i. e. have equivalent module categories. As an application, it is shown that the category of internal sup-lattices in a Grothendieck topos is equivalent to the module category over a suitable chosen ordinary quantale. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_11795 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Morita theory for quantales Mesablishvili, Bachuki Category Theory Quantum Algebra 18B25, 18C15, 18C20, 18D20, 18E08, 18F10, 18F75, 18M05 Morita theory for quantales is developed. The main result of the paper is a characterization of those quantaloids (categories enriched in the symmetric monoidal closed category of sup-lattices) that are equivalent to modular categories over quantales. Based on this characterization, necessary and sufficient conditions are derived for two quantales to be Morita-equivalent, i. e. have equivalent module categories. As an application, it is shown that the category of internal sup-lattices in a Grothendieck topos is equivalent to the module category over a suitable chosen ordinary quantale. |
| title | Morita theory for quantales |
| topic | Category Theory Quantum Algebra 18B25, 18C15, 18C20, 18D20, 18E08, 18F10, 18F75, 18M05 |
| url | https://arxiv.org/abs/2502.11795 |