MAGIC009: Category Theory

Course details

A core MAGIC course

Semester

Spring 2018
Monday, January 22nd to Friday, March 16th; Monday, April 23rd to Friday, May 4th

Hours

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

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

    Professor Michael Rathjen

    University
    University of Leeds

Bibliography

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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

The assessment for this course will be released on Monday 7th May 2018 and is due in by Sunday 20th May 2018 at 23:59.

The assessment for this course will be via a single take-home paper in May with 2 weeks to complete and submit online. There will be 4 questions. Each question will be marked out of 20. To pass the exam you will need ≥ 40 points out of the total of 80 points.

Please note that you are not registered for assessment on this course.

Files

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Lectures

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