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Internal factorisation systems
We introduce internal factorisation systems for internal categories. We recall the definitions and theory of internal categories and factorisation systems. We develop a diagrammatic calculus of pullbacks for ease of internal calculation. To define an internal factorisation system we define and study...
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| Format: | Thesis |
| Language: | English |
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Department of Mathematics and Applied Mathematics
2023
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| _version_ | 1867613224340291584 |
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| access_status_str | Open Access |
| author | Ranchod, Sanjiv |
| author2 | Janelidze, George |
| author_browse | Janelidze, George Ranchod, Sanjiv |
| author_facet | Janelidze, George Ranchod, Sanjiv |
| author_sort | Ranchod, Sanjiv |
| collection | Thesis |
| description | We introduce internal factorisation systems for internal categories. We recall the definitions and theory of internal categories and factorisation systems. We develop a diagrammatic calculus of pullbacks for ease of internal calculation. To define an internal factorisation system we define and study the subobjects of isomorphisms, an internalisation of the class of isomorphisms of a category. We provide an abstract example of an internal factorisation system. We then internalise various properties of factorisation systems, such as the two components determining each other, the cancellation properties and the essential uniqueness of factorisations, and show that an internal factorisation system satisfies these internal conditions. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/38111 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:32:44.899Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2023 |
| publishDateRange | 2023 |
| publishDateSort | 2023 |
| publisher | Department of Mathematics and Applied Mathematics |
| publisherStr | Department of Mathematics and Applied Mathematics |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/38111 Internal factorisation systems Ranchod, Sanjiv Janelidze, George Janelidze Tamar Mathematics and Applied Mathematics We introduce internal factorisation systems for internal categories. We recall the definitions and theory of internal categories and factorisation systems. We develop a diagrammatic calculus of pullbacks for ease of internal calculation. To define an internal factorisation system we define and study the subobjects of isomorphisms, an internalisation of the class of isomorphisms of a category. We provide an abstract example of an internal factorisation system. We then internalise various properties of factorisation systems, such as the two components determining each other, the cancellation properties and the essential uniqueness of factorisations, and show that an internal factorisation system satisfies these internal conditions. 2023-07-14T11:18:38Z 2023-07-14T11:18:38Z 2023 2023-07-14T11:18:20Z Master Thesis Masters MSc http://hdl.handle.net/11427/38111 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science |
| spellingShingle | Mathematics and Applied Mathematics Ranchod, Sanjiv Internal factorisation systems |
| thesis_degree_str | Master's |
| title | Internal factorisation systems |
| title_full | Internal factorisation systems |
| title_fullStr | Internal factorisation systems |
| title_full_unstemmed | Internal factorisation systems |
| title_short | Internal factorisation systems |
| title_sort | internal factorisation systems |
| topic | Mathematics and Applied Mathematics |
| url | http://hdl.handle.net/11427/38111 |
| work_keys_str_mv | AT ranchodsanjiv internalfactorisationsystems |