Category-theory-Spring-2010
From PLSwiki
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 Møgelberg (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
News
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 |
