The powerset monad on quantale-valued sets
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866929208302764032 |
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| author | Shen, Lili Zhao, Xiaojuan |
| author_facet | Shen, Lili Zhao, Xiaojuan |
| contents | For a small involutive quantaloid $\mathcal{Q}$, it is shown that the category of separated complete $\mathcal{Q}$-categories and left adjoint $\mathcal{Q}$-functors is strictly monadic over the category of symmetric $\mathcal{Q}$-categories. In particular, the (covariant) powerset monad on the category of quantale-valued sets is precisely formulated. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_03366 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The powerset monad on quantale-valued sets Shen, Lili Zhao, Xiaojuan Category Theory 06F07, 18D20, 18C15, 18C20 For a small involutive quantaloid $\mathcal{Q}$, it is shown that the category of separated complete $\mathcal{Q}$-categories and left adjoint $\mathcal{Q}$-functors is strictly monadic over the category of symmetric $\mathcal{Q}$-categories. In particular, the (covariant) powerset monad on the category of quantale-valued sets is precisely formulated. |
| title | The powerset monad on quantale-valued sets |
| topic | Category Theory 06F07, 18D20, 18C15, 18C20 |
| url | https://arxiv.org/abs/2401.03366 |