The bounded ideal monad on the category of quasi-metric spaces and its algebras
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909338257326080 |
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| author | Wang, Kai Zhang, Dexue |
| author_facet | Wang, Kai Zhang, Dexue |
| contents | The notion of bounded ideals is introduced for quasi-metric spaces. Such ideals give rise to a monad, the bounded ideal monad, on the category of quasi-metric spaces and non-expansive maps. Algebras of this monad are metric version of local dcpos of Mislove. It is shown that an algebra of the bounded ideal monad is a standard quasi-metric space of which the formal balls form a local dcpo; and that a continuous algebra is a standard quasi-metric space of which the formal balls form a local domain. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_04674 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The bounded ideal monad on the category of quasi-metric spaces and its algebras Wang, Kai Zhang, Dexue Category Theory 18D99 The notion of bounded ideals is introduced for quasi-metric spaces. Such ideals give rise to a monad, the bounded ideal monad, on the category of quasi-metric spaces and non-expansive maps. Algebras of this monad are metric version of local dcpos of Mislove. It is shown that an algebra of the bounded ideal monad is a standard quasi-metric space of which the formal balls form a local dcpo; and that a continuous algebra is a standard quasi-metric space of which the formal balls form a local domain. |
| title | The bounded ideal monad on the category of quasi-metric spaces and its algebras |
| topic | Category Theory 18D99 |
| url | https://arxiv.org/abs/2410.04674 |