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Ph.D. course on Category Theory, Spring 2010

Category theory, a branch of abstract algebra, has found many applications in mathematics, logic, and computer science, where it for example has been used to describe and analyse models of both sequential and parallel programming languages. Like such fields as elementary logic and set theory, category theory provides a basic conceptual apparatus and a collection of formal methods useful for addressing certain kinds of commonly occurring formal and informal problems, particularly those involving structural and functional considerations. This course is intended to acquaint students with these methods, and also to encourage them to reflect on the interrelations between category theory and the other basic formal disciplines. A number of applications of category theory to computer science will also be covered, including some recent developments.

This course is targetted at beginning Ph.d. students / M.Sc. students.

Literature: Steve Awodey: Category Theory. [SA]

Organizers: Lars Birkedal (LB), Rasmus M√łgelberg (REM)

Format: Regular course with lectures offered (once a week for 2 hours) by the organizers and other members of the PLS research group.

Credit: 7.5 ects, obtained by completing homeworks and an exam.

Meetings: We meet Fridays at 14-16 at the ITU room 4A14.

Evaluation: To pass, one must have four written assignments approved.

Participants: Mai Ajspur, Patrick Bahr, Maxime Beauquier, David Christiansen, Jonas Braband Jensen, Raghava Rao Mukkamala, Gian Perrone


Due to the FIRST seminar the lecture on April 16 has been moved to April 20 at 9-11 in 4A14.

More lectures have been moved to Tuesdays, see the schedule below. On Tuesdays we generally meet at 9-11. I expect that we can use 4A14, but I will have to check that (REM).

The remaining mandatory exercises will be due May 14 and June 4. They will appear on the homepage two weeks prior to these dates.

Topics and tentative plan

  • Below is a tentative plan.

Week Date Teacher Topic Materials Suggested exercises Mandatory exercises
01 Fri 05 Feb REM Introduction to categories [SA] Chapter 1 1.9.1, 1.9.2
02 Fri 12 Feb LB Abstract Structures [SA] Chapter 2 2.9.(1,2,6)
03 Fri 19 Feb REM Duality [SA] Chapter 3 3.5.(1,4,5)
04 Fri 26 Feb. OBS:10:00-12:00 TH Limits and colimits [SA] Chapter 5 - 5.3 1st assignment
05 Fri 05 Mar. OBS:10:00-12:00 TH Limits and colimits [SA] rest of Chapter 5
06 Fri 12 Mar Thamsborg Exponentials [SA] Chapter 6
07 Fri 19 Mar KS Functors and naturality [SA] Chapter 7 [1]
08 Fri 09 Apr KS Functors and naturality [SA] Chapter 7 2nd assignment
09 Fri 16 Apr (moved to April 20) REM Categories of diagrams [SA] Chapter 8
10 Fri 23 Apr REM Adjoints [SA] Chapter 9
11 Tue 27 Apr REM Adjoints [SA] Chapter 9 3rd assignment
12 Tue 04 May LB Regular Logic Notes
13 Fri 14 May Canceled 4th assignment
14 Fri 21 May REM Monads [SA] Chapter 10
15 Fri 28 May SD Reactive Systems Milner, Leifer: Deriving Bisimulation Congruences for Reactive System

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