Cartesian Differential Kleisli Categories
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866910328151867392 |
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| author | Lemay, Jean-Simon Pacaud |
| author_facet | Lemay, Jean-Simon Pacaud |
| contents | Cartesian differential categories come equipped with a differential combinator which axiomatizes the fundamental properties of the total derivative from differential calculus. The objective of this paper is to understand when the Kleisli category of a monad is a Cartesian differential category. We introduce Cartesian differential monads, which are monads whose Kleisli category is a Cartesian differential category by way of lifting the differential combinator from the base category. Examples of Cartesian differential monads include tangent bundle monads and reader monads. We give a precise characterization of Cartesian differential categories which are Kleisli categories of Cartesian differential monads using abstract Kleisli categories. We also show that the Eilenberg-Moore category of a Cartesian differential monad is a tangent category. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_06859 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Cartesian Differential Kleisli Categories Lemay, Jean-Simon Pacaud Category Theory Programming Languages 18F40, 18C20 F.3.2; F.4.1 Cartesian differential categories come equipped with a differential combinator which axiomatizes the fundamental properties of the total derivative from differential calculus. The objective of this paper is to understand when the Kleisli category of a monad is a Cartesian differential category. We introduce Cartesian differential monads, which are monads whose Kleisli category is a Cartesian differential category by way of lifting the differential combinator from the base category. Examples of Cartesian differential monads include tangent bundle monads and reader monads. We give a precise characterization of Cartesian differential categories which are Kleisli categories of Cartesian differential monads using abstract Kleisli categories. We also show that the Eilenberg-Moore category of a Cartesian differential monad is a tangent category. |
| title | Cartesian Differential Kleisli Categories |
| topic | Category Theory Programming Languages 18F40, 18C20 F.3.2; F.4.1 |
| url | https://arxiv.org/abs/2308.06859 |