Free Doubly-Infinitary Distributive Categories are Cartesian Closed
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915554146648064 |
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| author | Nunes, Fernando Lucatelli Vákár, Matthijs |
| author_facet | Nunes, Fernando Lucatelli Vákár, Matthijs |
| contents | We investigate categories in which products distribute over coproducts, a structure we call doubly-infinitary distributive categories. Through a range of examples, we explore how this notion relates to established concepts such as extensivity, infinitary distributivity, and cartesian closedness. We show that doubly-infinitary distributivity strictly strengthens the classical notion of infinitary distributivity. Moreover, we prove that free doubly-infinitary distributive categories are cartesian closed, unlike free distributive categories. The paper concludes with observations on non-canonical isomorphisms, alongside open questions and directions for future research. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_10447 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Free Doubly-Infinitary Distributive Categories are Cartesian Closed Nunes, Fernando Lucatelli Vákár, Matthijs Category Theory Logic in Computer Science Programming Languages Logic 18N15, 18C15, 18C20, 18D15, 18N10, 18D65, 18B50, 03F10, 03F03 We investigate categories in which products distribute over coproducts, a structure we call doubly-infinitary distributive categories. Through a range of examples, we explore how this notion relates to established concepts such as extensivity, infinitary distributivity, and cartesian closedness. We show that doubly-infinitary distributivity strictly strengthens the classical notion of infinitary distributivity. Moreover, we prove that free doubly-infinitary distributive categories are cartesian closed, unlike free distributive categories. The paper concludes with observations on non-canonical isomorphisms, alongside open questions and directions for future research. |
| title | Free Doubly-Infinitary Distributive Categories are Cartesian Closed |
| topic | Category Theory Logic in Computer Science Programming Languages Logic 18N15, 18C15, 18C20, 18D15, 18N10, 18D65, 18B50, 03F10, 03F03 |
| url | https://arxiv.org/abs/2403.10447 |