MAGIC009: Category Theory

Course details

A core MAGIC course

Semester

Spring 2019
Monday, January 21st to Friday, March 29th

Hours

Live lecture hours
10
Recorded lecture hours
0
Total advised study hours
40

Timetable

Thursdays
11:05 - 11:55

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.

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:
  1. Categories
  2. Functors and natural transformations
  3. Adjoints
  4. Limits
  5. Colimits
  6. Interaction between limits and adjoints
  7. Adjoint functor theorems
  8. Representables
  9. Presheaves and the Yoneda lemma
  10. Representables and limits

Lecturer

  • MR

    Prof Michael Rathjen

    University
    University of Leeds

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

Description

There are 2 weeks to complete and submit answers online. There are 4 questions. Each question will be marked out of 20. To pass the exam you will need at least 40 points out of the total of 80 points.

Assessment not available

Assessments are only visible to those being assessed for the course.

Files

Only consortium members have access to these files.

Please log in to view course materials.

Lectures

Please log in to view lecture recordings.