Properties of Arithmetic Universes and Locoi
| dc.contributor.author | Desrochers, Samuel | |
| dc.contributor.supervisor | Henry, Simon | |
| dc.contributor.supervisor | Scott, Philip J. | |
| dc.date.accessioned | 2025-11-28T22:18:50Z | |
| dc.date.available | 2025-11-28T22:18:50Z | |
| dc.date.issued | 2025-11-28 | |
| dc.description.abstract | In this thesis, we study two kinds of categories: locoi, which are lextensive categories with list objects, and arithmetic universes, which are pretoposes with list objects. We show three main results: first, if 𝒞 is a locos, then the list object functor 𝐿 : 𝒞 → 𝒞 is a polynomial functor. Second, if 𝒞 is a locos, then the full subcategory Fin(𝒞) of finite objects is a Boolean topos. Third, if 𝑆 is an arithmetic universe, then the free extension of 𝑆 by an object is the category [Finₛ, 𝕊] of indexed copresheaves on the internal category Finₛ of finite sets in 𝑆. | |
| dc.identifier.uri | http://hdl.handle.net/10393/51114 | |
| dc.identifier.uri | https://doi.org/10.20381/ruor-31569 | |
| dc.language.iso | en | |
| dc.publisher | Université d'Ottawa / University of Ottawa | |
| dc.subject | Category theory | |
| dc.title | Properties of Arithmetic Universes and Locoi | |
| dc.type | Thesis | en |
| thesis.degree.discipline | Sciences / Science | |
| thesis.degree.level | Doctoral | |
| thesis.degree.name | PhD | |
| uottawa.department | Mathématiques et statistique / Mathematics and Statistics |
