Saarland University Computer Science

Seminar: Category Theory Prof. Gert Smolka, Steven Schäfer, Yannick Forster, Jonas Kaiser, Kathrin Stark, Dominik Kirst

Seminar, 7 credit points, Summer Semester 2017



Write-up submission

This is just a reminder that the deadline for the submission of your write-up is tomorrow, September 20th. Please submit by opening a pull request on Github and not by email. You can contact us if you have technical problems.


New Material

We just uploaded the following: Solutions for Sheet 11 | Exercise Sheet 12 | Slides of Talk 12


Sheet 9

We have just published the exercise sheet for talk 9 from Joachim bard.


Talk 6

We just uploaded the exercise sheet for talk 6, as well as the corresponding slides of the talk. Both can be found under Materials.


Exercise Sheet from Session 5 now online

We have uploaded the exercise sheet from Mostafa.


Solution 3 now online

The Solution to the third exercise sheet is now available in the materials section


Solution 4 now online

A first version of the sample solutions for Sarah's exercise sheet 4 is available under Materials.


Sheet 4 -- new version

There is an updated version of sheet 4 available, which fixes a few minor errors in exercise 4.1. The new version can be found under materials.


Exercise Sheet from Session 4 now online

Hi, I just uploaded the exercise sheet that Sarah prepared for her talk on last Wednesday. Please remember to work through at least some of the posed questions. Bring your answers along next week, so that we can have a productive discussion :-) -- the CT team


Solution 2 now online

We just uploaded, with some delay, the solutions to the second exercise sheet.


Exercise Sheet 3 online

We just uploaded the third exercise sheet. -- the CT team


Info Slides from Session 3 online

I just uploaded the info slides from the session yesterday. I also included the remark that your phase 2 presentations should be around 40 minutes. -- Jonas


Exercise Sheet 2 online

We have just uploaded the exercise prepared by the second group of phase 1. You find it under Materials.


Topic Assigments

The topics for Phase 2 have been assigned. Please refer to the Topics page (visible after login) to find out which topic was assigned to you and who your advisor is going to be.

The CT-team

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In this seminar we present a gentle introduction to category theory. No prior knowledge of category theory is assumed but a certain degree of mathematical competence (e.g. MFI2) is essential. There are no further mandatory prerequisites.

During the seminar we will encounter a number of increasingly abstract concepts. Our goal is to enable the students to understand the intuitions behind these ideas and then confidently reason about them.

The seminar is geared towards the notion of categorical logic and categorical semantics, with a categorical model for the simply typed lambda calculus as our first major milestone. We are going to use a type theoretic foundation and whenever we have to make something absolutely precise we are going to fall back to its language. Thus any background in type theory (e.g. ICL) is certainly beneficial, though strictly optional.

Apart from the theoretical content itself our students will also learn how to efficiently communicate complex topics, both verbally and in writing, to a group of peers.


Kick-Off Meeting: Thursday, 20.04.2017, 16:15, E1 3, R528


Grading and Expected Workload

The seminar will consist of two phases. In the first phase we are going to develop the core principles, definitions and terminology that underpin category theory. This will take place during the first three weeks of the seminar where you work in small groups. For the second phase we have selected a sequence of topics that form a comprehensive introduction to basic category theory. Each student will be assigned one of these topics to prepare, present and discuss and subsequently write up in a coherent fashion. Note that we expect everybody to read the core material for each week. Most topics heavily rely on the preceding sessions.

To obtain the 7 CP of the seminar, we expect the following from each participant:

Phase 1:

In a group of three students, prepare one of the three introductory topics. This includes the following:

  • Carefully read the assigned core and auxiliary material before the session.
  • Prepare an exercise sheet that tests the covered topics of your material. This will be handed to the class after your presentation and should take about 2 to 3 hours to complete.
  • Present the prepared material and lead the discussion in class. This includes prompting for and answering questions of your audience.
  • Write up your material as a coherent chapter of at most 10 pages. This has to be handed in before the end of the teaching period (July, 29th).

Phase 2:

We expect everybody to read the core material each week and actively participate in the discussion. Each student is in charge of one particular topic. He should additionally do the following for his assigned session:

  • Carefully read and prepare the core and auxiliary material.
  • Prepare a 45 min talk/lecture on the assigned material.
  • Prepare an exercise sheet on the covered topics that should take at most 2 to 3 hours complete. This is again handed out at the end of the respective session.
  • Meet with the assigned instructor in the week prior to the session to discuss the plan for the lecture and answer open questions. The meeting is compulsory and should be scheduled early enough to be able to incorporate feedback into the session preparation.
  • Give the presentation/lecture on the assigned material and lead the subsequent discussion.
  • Write up a chapter, approximately 10 pages, on the assigned topic. This has to be submitted prior to September, 20th.

General Remarks

The covered material is mostly foundational so we believe that presentations in lecture-style are ideal to convey the key points. The subsequent discussions in class are essential to ensure that everybody grasps the key concepts. We also hope to aggregate your write-ups into a single cohesive introductory text, hence we refer to them above as chapters. For this purpose, we are going to provide a git repository and uniform style sheets and you can rely on the definitions from your colleagues in earlier chapters.

The primary aspects of your grade are:

  • How well did you present your assigned material in class?
  • Did you actively participate during the whole seminar (not just in your assigned session)?
  • How well did you write up your assigned chapter?