Ultracategories via Kan extensions of relative monads
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916790701916160 |
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| author | Tarantino, Umberto Wrigley, Joshua |
| author_facet | Tarantino, Umberto Wrigley, Joshua |
| contents | Many structured categories of interest are most naturally described as algebras for a relative monad, but turn out nonetheless to be algebras for an ordinary monad. We show that, under suitable hypotheses, the left oplax Kan extension of a relative 2-monad on categories yields a pseudomonad having the same category of colax algebras. In particular, we apply this to the study of ultracategories to recover the 'ultracompletion' pseudomonad. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_09788 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ultracategories via Kan extensions of relative monads Tarantino, Umberto Wrigley, Joshua Category Theory 18N15 (Primary) 18C15, 18C20, 03G30, 03C20 (Secondary) Many structured categories of interest are most naturally described as algebras for a relative monad, but turn out nonetheless to be algebras for an ordinary monad. We show that, under suitable hypotheses, the left oplax Kan extension of a relative 2-monad on categories yields a pseudomonad having the same category of colax algebras. In particular, we apply this to the study of ultracategories to recover the 'ultracompletion' pseudomonad. |
| title | Ultracategories via Kan extensions of relative monads |
| topic | Category Theory 18N15 (Primary) 18C15, 18C20, 03G30, 03C20 (Secondary) |
| url | https://arxiv.org/abs/2506.09788 |