Full Text Available
Note: Clicking the button above will open the full text document at the original institutional repository in a new window.
Topics in 2-categorical Algebra
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- c...
Saved in:
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Thesis |
| Language: | English |
| Published: |
Department of Mathematics and Applied Mathematics
2024
|
| Subjects: | |
| Tags: |
No Tags, Be the first to tag this record!
|
| _version_ | 1867614360762843136 |
|---|---|
| access_status_str | Open Access |
| author | Sutton, Matthew |
| author2 | Janelidze, George |
| author_browse | Janelidze, George Sutton, Matthew |
| author_facet | Janelidze, George Sutton, Matthew |
| author_sort | Sutton, Matthew |
| collection | Thesis |
| description | 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. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/39858 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:50:48.810Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2024 |
| publishDateRange | 2024 |
| publishDateSort | 2024 |
| 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:11427/39858 Topics in 2-categorical Algebra Sutton, Matthew Janelidze, George Mathematics and Applied Mathematics 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. 2024-06-05T12:35:02Z 2024-06-05T12:35:02Z 2023 2024-06-05T12:20:24Z Thesis / Dissertation Masters MSc http://hdl.handle.net/11427/39858 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science |
| spellingShingle | Mathematics and Applied Mathematics Sutton, Matthew Topics in 2-categorical Algebra |
| thesis_degree_str | Master's |
| title | Topics in 2-categorical Algebra |
| title_full | Topics in 2-categorical Algebra |
| title_fullStr | Topics in 2-categorical Algebra |
| title_full_unstemmed | Topics in 2-categorical Algebra |
| title_short | Topics in 2-categorical Algebra |
| title_sort | topics in 2 categorical algebra |
| topic | Mathematics and Applied Mathematics |
| url | http://hdl.handle.net/11427/39858 |
| work_keys_str_mv | AT suttonmatthew topicsin2categoricalalgebra |