Course details
A core MAGIC course
Semester
 Autumn 2010
 Monday, October 4th to Friday, December 17th
Hours
 Live lecture hours
 10
 Recorded lecture hours
 0
 Total advised study hours
 0
Timetable
 Fridays
 09:05  09:55
Announcements
The second lecture, on Friday 15th October, will be given by Dr Vanessa Miemietz (UEA).
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.
Prerequisites
There 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.
Syllabus
The topics covered are:
 Categories: definitions, examples, special kinds of arrows and objects, duality
 Functors: definitions, examples, full and faithful functors, subcategories, Homfunctors, 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 and creation: right adjoints preserve limits, general adjoint functor theorem, examples
Lecturer

JK
Dr Jonathan Kirby
 University
 University of East Anglia
Bibliography
Follow the link for a book to take you to the relevant Google Book Search page
You may be able to preview the book there and 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.
Assessment
Attention needed
Assessment information will be available nearer the time.
Lectures
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