## Category Theory (MAGIC009) |

## GeneralThis course is part of the MAGIC core. Description
Category theory is the language of much of modern mathematics. It starts from the observation that the collection of all mathematical structures of a certain kind may itself be viewed as a mathematical object - a category. This is an introductory course in category theory. The main theme will be universal properties in their various manifestations, one of the most important uses of categories in mathematics.
Semester
Spring 2012 (Monday, January 16 to Friday, March 23) Timetable
- Mon 10:05 - 10:55
## Students
## PrerequisitesThere are few formal prerequisites to the material. However, I will be giving examples from mathematics to motivate the ideas and demonstrate how they are used, so an undergraduate degree in mathematics (rather than for example computer science or philosophy) would be an advantage. In particular, I will assume some knowledge of algebra such as vector spaces and their bases, and groups, but undergraduate level knowledge of these subjects is sufficient.
## SyllabusThe topics covered are:
- Categories: definitions, examples, special kinds of arrows and objects, duality
- Functors: definitions, examples, full and faithful functors, subcategories, Hom-functors, contravariant functors
- Universal properties: examples including vector space bases, fields of fractions, tensor products, quotients, products, and coproducts
- Natural transformations: definitions and examples, functor categories, equivalence of categories, horizontal composition
- Limits: examples, general definition, computing limits in Set, complete categories
- Colimits: definition, examples, computing colimits in Set
- Adjunctions: vector space bases, formal definition, examples, unit and counit
- Limit preservation: right adjoints preserve limits
- Limit creation: general adjoint functor theorem, examples
- The category of Sets
## Bibliography
Note:
Clicking on the link for a book will take you to the relevant Google Book Search page. You may be able to preview the book there. On the right hand side you will see links to places where you can buy the book. There is also link marked 'Find this book in a library'. This sometimes works well, but not always. (You will need to enter your location, but it will be saved after you do that for the first time.) ## AssessmentThe course will be assessed by a single exam. The paper is available under the Assignments tab, and the deadline is 13th April 2012.
## AssignmentsExam for MAGIC009: Category Theory Spring 2012
## FilesFiles marked |