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Extensivity relative to a bifunctor
Thesis (PhD)--Stellenbosch University, 2026.
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| Format: | Thesis |
| Language: | English |
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Stellenbosch : Stellenbosch University
2026
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| _version_ | 1867614110315708416 |
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| access_status_str | Open Access |
| author | Theart, Emma |
| author2 | Hoefnagel, Michael |
| author_browse | Hoefnagel, Michael Theart, Emma |
| author_facet | Hoefnagel, Michael Theart, Emma |
| author_sort | Theart, Emma |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description | Thesis (PhD)--Stellenbosch University, 2026. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/135773 |
| institution | Stellenbosch University (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:46:49.940Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2026 |
| publishDateRange | 2026 |
| publishDateSort | 2026 |
| publisher | Stellenbosch : Stellenbosch University |
| publisherStr | Stellenbosch : Stellenbosch University |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/135773 Extensivity relative to a bifunctor Theart, Emma Hoefnagel, Michael Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. Thesis (PhD)--Stellenbosch University, 2026. Theart, E. 2026. Extensivity relative to a bifunctor. Unpublished doctoral dissertation. Stellenbosch: Stellenbosch University [online]. Available: https://scholar.sun.ac.za/items/e71456b9-3ba6-4e13-8155-80d6d08eee65 Extensive categories capture a fundamental feature of the category of sets: their coproducts are both disjoint and universal. Two equivalent formulations of extensive categories provide two distinct perspectives on the notion. The first is as a property of functors, and the second as a property of morphisms in the category. This thesis explores both perspectives. The morphism-focused viewpoint is captured through extensive morphisms, which allow one to study extensivity in categories that are not themselves extensive. From the functorial viewpoint, we introduce near-sums, functorial replacements for coproducts in categories lacking them. Near-sums provide a natural setting for extending the theory of extensive categories, capturing key features thereof, such as disjointness and universality. Doctoral 2026-04-10T06:41:30Z 2026-04-10T06:41:30Z 2026-03 Thesis https://scholar.sun.ac.za/handle/10019.1/135773 en Stellenbosch University 112 pages application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | Theart, Emma Extensivity relative to a bifunctor |
| title | Extensivity relative to a bifunctor |
| title_full | Extensivity relative to a bifunctor |
| title_fullStr | Extensivity relative to a bifunctor |
| title_full_unstemmed | Extensivity relative to a bifunctor |
| title_short | Extensivity relative to a bifunctor |
| title_sort | extensivity relative to a bifunctor |
| url | https://scholar.sun.ac.za/handle/10019.1/135773 |
| work_keys_str_mv | AT theartemma extensivityrelativetoabifunctor |