Internal factorisation systems
| dc.contributor.advisor | Janelidze, George | |
| dc.contributor.advisor | Janelidze Tamar | |
| dc.contributor.author | Ranchod, Sanjiv | |
| dc.date.accessioned | 2023-07-14T11:18:38Z | |
| dc.date.available | 2023-07-14T11:18:38Z | |
| dc.date.issued | 2023 | |
| dc.date.updated | 2023-07-14T11:18:20Z | |
| dc.description.abstract | 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. | |
| dc.identifier.apacitation | Ranchod, S. (2023). <i>Internal factorisation systems</i>. (). ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/38111 | en_ZA |
| dc.identifier.chicagocitation | Ranchod, Sanjiv. <i>"Internal factorisation systems."</i> ., ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2023. http://hdl.handle.net/11427/38111 | en_ZA |
| dc.identifier.citation | Ranchod, S. 2023. Internal factorisation systems. . ,Faculty of Science ,Department of Mathematics and Applied Mathematics. http://hdl.handle.net/11427/38111 | en_ZA |
| dc.identifier.ris | TY - Master Thesis AU - Ranchod, Sanjiv AB - 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. DA - 2023_ DB - OpenUCT DP - University of Cape Town KW - Mathematics and Applied Mathematics LK - https://open.uct.ac.za PY - 2023 T1 - Internal factorisation systems TI - Internal factorisation systems UR - http://hdl.handle.net/11427/38111 ER - | en_ZA |
| dc.identifier.uri | http://hdl.handle.net/11427/38111 | |
| dc.identifier.vancouvercitation | Ranchod S. Internal factorisation systems. []. ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2023 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/38111 | en_ZA |
| dc.language.rfc3066 | eng | |
| dc.publisher.department | Department of Mathematics and Applied Mathematics | |
| dc.publisher.faculty | Faculty of Science | |
| dc.subject | Mathematics and Applied Mathematics | |
| dc.title | Internal factorisation systems | |
| dc.type | Master Thesis | |
| dc.type.qualificationlevel | Masters | |
| dc.type.qualificationlevel | MSc |