Course syllabus

Jump to today

Welcome to Category Theory, LOG350, 7,5 credits, Fall 2023

This course is both part of the Master's Programme in Logic (Links to an external site.) as well as available as a free standing course. 

The course syllabus is available here: course syllabus.

Course content

The course starts with general category theory and defines the concept of a category. Then, a number of central structures within categories, defined by using abstract limits and universal properties, are presented. The course continues onto concepts outside categories: functors, natural transformations, adjunctions, presheaves and the Yoneda lemma. The course also provides an introduction to topos theory, and its connection to logic.

Meetings

We will have 8 meetings. Each will correspond to parts of Leinster (L) or Smith (S). The students are expected to have read the indicated material before the meeting.

  1. Introduction & Categories (S Ch. 1-4)
  2. Some Structures in Categories (S Ch. 7,8,10,15; the ones in between can be helpful)
  3. Limits & Colimits (S 18-20) [presented by Yichi]
  4. Exponentials & Cartesian Closed Categories (S Ch. 16,17) [presented by Sikai]
  5. Toposes (S Ch. 21-24) [presented by Fong Yuan]
  6. Functors & Natural Transformations (L Ch. 1.2-1.3) [presented by Caroline]
  7. Presheaves & Yoneda Lemma (L Ch. 4)
  8. Adjoints (L Ch. 2)

Course Literature

The main references for the course are Tom Leinster's "Basic Category Theory" and Peter Smith's notes on category theory.

There are many more introductory books and lecture notes, many of them freely accessible on the internet. Students are encouraged to consult these as they see fit.

Examination

The course is examined in three ways:

  • Presentations: Each student will give a presentation of 70 minutes on a topic. After the presentation, there will be a 20 minutes Q&A and discussion session, lead by the student. The presentation decides if the student will get a "VG"
  • Handouts: There will be two handouts with exercises the students will need to solve. The students will need to achieve a certain percentage of points on each to pass. They will be due on the [insert data] and [insert data]. Students will have at least 2 weeks to work on them. The solutions will need to be typeset in LaTeX and submitted via Canvas.
  • Attendance: To pass, a student must attend most of the student presentations.

Other resources

The tikz-cd package can be used to typeset commutative diagrams in LaTeX. There are at least two browser applications that help creating tikzcd environments.

nLab is an online wiki for researchers of higher category theory. While many articles may quickly get too advanced for beginners, it can sometimes prove a useful source of references for further reading.

Teachers

The course will be taught by Dominik Wehr. You can contact him by email, dominik.wehr@gu.se. Examiner is [insert data]. 

Registration

You can find information regarding registration here (Links to an external site.).

Schedule

The schedule for the course is available through TimeEdit.

Learning outcomes

See the course syllabus (Links to an external site.) for more information.

Special pedagogical support

If you have a disability and are in need of special pedagogical support please see the information available at the student portal (Links to an external site.). 

Contact information

  • Course Coordinator Dominik Wehr, dominik.wehr@gu.se answers questions about the course content, literature and schedule.
  • Education Administrator Peter Olsson, peter.olsson.2@gu.se answers questions about registration, examination administration, study interruptions, study breaks, certificates, etc. 
  • Masters Program Coordinator Rasmus Blanck, rasmus.blanck@gu.se, is responsible for programme issues and study guidance for students of the programme.
  • Education Coordinator Peter Johnsen, peter.johnsen@gu.se

Course summary:

Course Summary
Date Details Due