Course syllabus

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Welcome to Category Theory, LOG350, 7,5 credits, Fall 2022

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.

Presentations

Each student will present on one topic. Unless specified otherwise, all chapter specifications refer to McLarty's "Elementary Categories, Elementary Toposes".

  1. Simple Structures in Categories (presented by Aleksandar) [Chap. 1.3-1.5, 4.1, 2.1-2.4]
  2. Limits & Colimits (presented by Kirsten) [Chap. 2.5-2.6, 4.2-4.6]
  3. Exponentials (presented by Julius) [Chap. 6]
  4. Functors & Natural transformations (presented by Camila) [Chap. 8, 9]
  5. Adjunctions (presented by Orvar) [Chap. 10]
  6. Foundational Issues of Category Theory (presented by Yoann) [Chap. 12]
  7. Presheaves & Yoneda Lemma (presented by André) [Leinster Chap. 4]
  8. Elementary Topoi & Natural Number Objects (presented by Oskar) [Chap. 13, 19]
  9. Topos Logic (presented by Armand) [Chap. 14, 15, 16]

Course Literature

The main reference for the course is Colin McLarty's "Elementary Categories, Elementary Toposes".

Because McLarty does not provide many illustrating examples, we furthermore recommend students also consult other introductions to category theory. Two particularly good books which are freely accessible are:

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 2.12.2022 and 13.1.2023. 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 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 Fredrik Engström, fredrik.engstrom@gu.se. 

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 Fredrik Engström, fredrik.engstrom@gu.se is responsible for programme issues and study guidance for students of the programme.
  • Student counselor Peter Johnsen, peter.johnsen@gu.se, is responsible for study guidance of the free-standing course.

Course summary:

Course Summary
Date Details Due