Course details
A core MAGIC course
Semester
 Autumn 2013
 Monday, October 7th to Saturday, December 14th
Hours
 Live lecture hours
 10
 Recorded lecture hours
 0
 Total advised study hours
 0
Timetable
 Mondays
 10:05  10:55
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.
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
Category theory is an abstract algebraic point of view of mathematics. Some familiarity with an algebraic way of thinking is important. It is therefore an advantage to have studied an undergraduate course in group theory or ring theory, or some other abstract algebra course. I will assume some knowledge of algebra such as vector spaces and their bases, and groups, but a basic 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: right adjoints preserve limits
 Limit creation: general adjoint functor theorem, examples
 The category of Sets
Lecturer

JK
Dr Jonathan Kirby
 University
 University of East Anglia
Bibliography
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Assessment
Description
The assessment for this course will be via a single takehome paper in January and with 2 weeks to complete and submit online. The intention is that a student who has studied throughout the term will be able to pass by spending 2 hours on the exam.
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Lectures
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