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Sums and covers in categories
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_ | 1867613904663740416 |
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| access_status_str | Open Access |
| author | Ferguson, Roy Angus |
| author2 | Janelidze, Zurab |
| author_browse | Ferguson, Roy Angus Janelidze, Zurab |
| author_facet | Janelidze, Zurab Ferguson, Roy Angus |
| author_sort | Ferguson, Roy Angus |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description | Thesis (PhD)--Stellenbosch University, 2026. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/135984 |
| institution | Stellenbosch University (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:43:33.723Z |
| 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:10019.1/135984 Sums and covers in categories Ferguson, Roy Angus Janelidze, Zurab Hoefnagel, Michael Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. Thesis (PhD)--Stellenbosch University, 2026. Ferguson, R. A. 2026. Sums and covers in categories. Unpublished doctoral dissertation. Stellenbosch: Stellenbosch University [online]. Available: https://scholar.sun.ac.za/items/65637688-e644-491a-a259-be18cd8be44e A cover of an object X can be seen from two points of view. In the one point of view, it is a suitable sink with codomain X. On the other hand, we can see a cover of X as a collection of parts which add up to make X. These two perspectives come together in the structure of a coproduct. This notion of a cover generalises to a sum structure in the sense of Zurab Janelidze. We study covers and sums at this level, abstracting a number of results and constructions known for coproducts. We examine the dual notion of a product structure and show that these coincide with independence structures of Alex Simpson. We show that morphisms from sum structures to product structures exhibit matrix representations. We study extensivity for sum structures, and focus on extensivity relative to cover-reflecting morphisms. We introduce and explore a new class of morphisms, called monilmorphisms, and use them to construct examples of sum structures exhibiting precisely the said form relative extensivity. We conclude by departing from covers determined by sums, and study Grothendieck topologies as special kinds of functors called forms. Doctoral 2026-04-17T07:14:21Z 2026-04-17T07:14:21Z 2026-03 Thesis https://scholar.sun.ac.za/handle/10019.1/135984 en Stellenbosch University 193 pages application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | Ferguson, Roy Angus Sums and covers in categories |
| title | Sums and covers in categories |
| title_full | Sums and covers in categories |
| title_fullStr | Sums and covers in categories |
| title_full_unstemmed | Sums and covers in categories |
| title_short | Sums and covers in categories |
| title_sort | sums and covers in categories |
| url | https://scholar.sun.ac.za/handle/10019.1/135984 |
| work_keys_str_mv | AT fergusonroyangus sumsandcoversincategories |