Topics in 2-categorical Algebra
| dc.contributor.advisor | Janelidze, George | |
| dc.contributor.author | Sutton, Matthew | |
| dc.date.accessioned | 2024-06-05T12:35:02Z | |
| dc.date.available | 2024-06-05T12:35:02Z | |
| dc.date.issued | 2023 | |
| dc.date.updated | 2024-06-05T12:20:24Z | |
| dc.description.abstract | In this thesis we will examine 2-categories and higher categorical structures and formulate 1-categorical theorems in the language of higher categories as well as formulate some internal definitions of these base structures in finitely complete categories. We will begin by defining the relevant 2- categorical structures, such as 2-categories, double categories, bicategories and enriched categories, as well as examples of all. Following this, we will show first how these structures relate to each other (for instance, a 2-category is a special case of a double category) and then demonstrate that the category of V-enriched categories forms a 2-category. Chapter 2 begins with the definition of internal categories in a category C with pullbacks, as well as internal functors and internal natural transformations, after which we will demonstrate that the category of internal categories forms a 2-category. We will then show that in C with pullbacks and terminal object, one can define an internal 2-category and an internal bicategory , and show that these are the same as small 2-categories and small bicategories in the case of C = Set. In the final chapter, we demonstrate that some of the familiar constructions of 1-category theory can actually be defined in a 2-category, and certain theorems about these structures proven using only 2-categorical methods. | |
| dc.identifier.apacitation | Sutton, M. (2023). <i>Topics in 2-categorical Algebra</i>. (). ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/39858 | en_ZA |
| dc.identifier.chicagocitation | Sutton, Matthew. <i>"Topics in 2-categorical Algebra."</i> ., ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2023. http://hdl.handle.net/11427/39858 | en_ZA |
| dc.identifier.citation | Sutton, M. 2023. Topics in 2-categorical Algebra. . ,Faculty of Science ,Department of Mathematics and Applied Mathematics. http://hdl.handle.net/11427/39858 | en_ZA |
| dc.identifier.ris | TY - Thesis / Dissertation AU - Sutton, Matthew AB - In this thesis we will examine 2-categories and higher categorical structures and formulate 1-categorical theorems in the language of higher categories as well as formulate some internal definitions of these base structures in finitely complete categories. We will begin by defining the relevant 2- categorical structures, such as 2-categories, double categories, bicategories and enriched categories, as well as examples of all. Following this, we will show first how these structures relate to each other (for instance, a 2-category is a special case of a double category) and then demonstrate that the category of V-enriched categories forms a 2-category. Chapter 2 begins with the definition of internal categories in a category C with pullbacks, as well as internal functors and internal natural transformations, after which we will demonstrate that the category of internal categories forms a 2-category. We will then show that in C with pullbacks and terminal object, one can define an internal 2-category and an internal bicategory , and show that these are the same as small 2-categories and small bicategories in the case of C = Set. In the final chapter, we demonstrate that some of the familiar constructions of 1-category theory can actually be defined in a 2-category, and certain theorems about these structures proven using only 2-categorical methods. DA - 2023 DB - OpenUCT DP - University of Cape Town KW - Mathematics and Applied Mathematics LK - https://open.uct.ac.za PY - 2023 T1 - Topics in 2-categorical Algebra TI - Topics in 2-categorical Algebra UR - http://hdl.handle.net/11427/39858 ER - | en_ZA |
| dc.identifier.uri | http://hdl.handle.net/11427/39858 | |
| dc.identifier.vancouvercitation | Sutton M. Topics in 2-categorical Algebra. []. ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2023 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/39858 | 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 | Topics in 2-categorical Algebra | |
| dc.type | Thesis / Dissertation | |
| dc.type.qualificationlevel | Masters | |
| dc.type.qualificationlevel | MSc |