Abstract Kleisli Structures on 2-categories
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915511895326720 |
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| author | Miranda, Adrian |
| author_facet | Miranda, Adrian |
| contents | Fuhrmann introduced Abstract Kleisli structures to model call-by-value programming languages with side effects, and showed that they correspond to monads satisfying a certain equalising condition on the unit. We first extend this theory to non-strict morphisms of monads, and to incorporate 2-cells of monads. We then further extend this to a theory of abstract Kleisli structures on 2-categories, characterising when the original pseudomonad can be recovered by the abstract Kleisli structure on its 2-category of free-pseudoalgebras.
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| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_00900 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Abstract Kleisli Structures on 2-categories Miranda, Adrian Category Theory Fuhrmann introduced Abstract Kleisli structures to model call-by-value programming languages with side effects, and showed that they correspond to monads satisfying a certain equalising condition on the unit. We first extend this theory to non-strict morphisms of monads, and to incorporate 2-cells of monads. We then further extend this to a theory of abstract Kleisli structures on 2-categories, characterising when the original pseudomonad can be recovered by the abstract Kleisli structure on its 2-category of free-pseudoalgebras. |
| title | Abstract Kleisli Structures on 2-categories |
| topic | Category Theory |
| url | https://arxiv.org/abs/2404.00900 |