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General


This 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 2019 (Monday, January 21 to Friday, March 29)

Hours

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

Timetable

  • Thu 11:05 - 11:55

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


Michael Rathjen
Email M.Rathjen@leeds.ac.uk
Phone +44 (0)113 3435109


Bibliography


Categories for the working mathematicianMac Lane
Basic Category TheoryLeinster


Note:

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Assessment



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.

Category Theory Exam 2018-19

Files:Exam paper
Released: Sunday 28 April 2019 (148.3 days ago)
Deadline: Sunday 12 May 2019 (133.3 days ago)


Files


Files marked L are intended to be displayed on the main screen during lectures.

Week(s)File
1-20ct-exam_2019.pdf
1-15ct-lecture1_handout.pdfL
1-15ctlecture10_handout.pdfL
1-15ctlecture2_handout.pdfL
1-15ctlecture3_handout.pdfL
1-15ctlecture4_handout.pdfL
1-15ctlecture5_handout.pdfL
1-15ctlecture6_handout.pdfL
1-15ctlecture7_handout.pdfL
1-15ctlecture8_handout.pdfL
1-15ctlecture9_handout.pdfL


Recorded Lectures


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