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

Seminar, 7 credit points, Summer Semester 2017

Overview 

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?