Main Page

News

Evaluation

Written on 09.08.22 by Michael Sammler

Hi,
the results of the evaluation are now available on the Materials page. Thank you that so many of you filled out the evaluation and gave feedback!

Session 14

Written on 18.07.22 by Michael Sammler

Hi,

in the next session (session 14 on 22.7.), Andrew will present solutions to the exercises and then discuss how the material of this course fits into the bigger picture. As usual, we encourage you to do the exercises yourself before the lecture such that we can have an interesting discussion.

Homework 14

Written on 15.07.22 by Michael Sammler

Hello everyone,

the new exercise sheet (and also the last exercise sheet of this seminar) is now available on the materials page.

Enjoy!

Homework 13

Written on 08.07.22 by Michael Sammler

Hello everyone,

the new exercise sheet is now available on the materials page.

Enjoy!

Homework 12

Written on 01.07.22 by Michael Sammler

Hello everyone,

the new exercise sheet is now available on the materials page.

Enjoy!

A result you can use in the current homework

Written on 29.06.22 by Andrew Hirsch

In problem 4 of homework 11, feel free to use the following result: if F and G are two halves of an equivalence of category, than both F and G preserve both products and exponentials.

Hopefully you'll find that result useful!

New Homwork

Written on 24.06.22 by Jan Menz

Hello everyone,

we uploaded the new exercise sheet. As always, you can find it on the materials page.

Enjoy.

Added chapter 8.8 to the reading of 1.7. (next week)

Written on 22.06.22 by Michael Sammler

Hi everyone,

we decided to add chapter 8.8 to the reading for 1.7. (i.e. next week) as its topic is important for many CS and logic applications. The main page of the CMS has been updated accordingly.

Homework 10

Written on 17.06.22 by Jan Menz

Hello everyone,

the new exercise sheet as well as the recording of todays seminar are now available on the materials page.

Enjoy!

Homework 9

Written on 10.06.22 by Michael Sammler

Hello everyone,

homework 9 and the slides from the class today are now available on the Materials page. The recording of the lecture should follow soon. Enjoy!

Homework 8

Written on 03.06.22 by Michael Sammler

Hello everyone,

homework 8 is now available on the Materials page. Enjoy!

Homework 7

Written on 27.05.22 by Jan Menz

Hello everyone,

homework 7 is now available on the Materials page. Enjoy!

New Homework

Written on 20.05.22 by Michael Sammler

Hello everyone,

the new homework is available on the materials page now. The recording of the lecture today will follow shortly. Enjoy!

New Homework

Written on 13.05.22 by Michael Sammler

Hello everyone,

the new homework, the recording of the lecture today, and the notes from the semantics course are available on the materials page now. Enjoy!

Room on 13.5. as usual

Written on 10.05.22 by Michael Sammler

Hi everyone,

The seminar this week (i.e. 13.5.) will be held in the same room as usual i.e. room 029 in MPI-SWS (E 1.5). (Previously it was not clear whether we would be able to use this room this Friday, but now we know that we can actually use it.)

New Homework

Written on 06.05.22 by Jan Menz

Hello everyone,

the new homework is available on the materials page now. Enjoy!

Lecture today (6.5.) starting 10 minutes late

Written on 06.05.22 by Michael Sammler

Hi everyone, the lecture today (6.5.) will start roughly 10 min late (i.e. around 10:10) due to a delay.

Changing topics

Written on 03.05.22 by Michael Sammler

Hi everyone,

if you would like to change your topic, please find another student who would like to swap their topic with you and send us an email. If you are looking for someone to swap topics with, you can post a message on the discourse.

Topic assignment, discourse and new homework

Written on 29.04.22 by Michael Sammler

Hi everyone,

The assignment of the topics and scribes can be found at the bottom of the Main page (https://cms.sic.saarland/ct22/). You can also find your topic on https://cms.sic.saarland/ct22/students/view .

The discourse is available at https://category-seminar-discourse.mpi-sws.org/ .

The… Read more

Hi everyone,

The assignment of the topics and scribes can be found at the bottom of the Main page (https://cms.sic.saarland/ct22/). You can also find your topic on https://cms.sic.saarland/ct22/students/view .

The discourse is available at https://category-seminar-discourse.mpi-sws.org/ .

The homework for the next week and the solution for sheet 1 is available from the materials. The solutions for sheet 2 and the notes from the lecture today will follow soon (hopefully this afternoon).

Room for Seminar

Written on 28.04.22 by Jan Menz

Hello everyone,

as announced last week, the Category Theory Seminar is going hybrid. This means that, should you wish to, you can participate in person starting tomorrow.

The seminar will take place in room 029 in MPI-SWS (E 1.5).

We will not have this room on May 13th. We will let you know… Read more

Hello everyone,

as announced last week, the Category Theory Seminar is going hybrid. This means that, should you wish to, you can participate in person starting tomorrow.

The seminar will take place in room 029 in MPI-SWS (E 1.5).

We will not have this room on May 13th. We will let you know where the seminar takes place on that date in due time.

Assignment of topics

Written on 26.04.22 by Michael Sammler

Hi, everyone.

We have updated the list of topics on the main site of the CMS. Now it is your turn to decide about which of the topics you are interested in leading the discussion! As a reminder, each student who is officially taking the course needs to lead the discussion of one topic. (If you are… Read more

Hi, everyone.

We will handle the assignment of topics via the tutorial assignment system of the CMS. The process for you works as follows:
1. Look at the list of topics at https://cms.sic.saarland/ct22/ and decide which you do (not) want to lead.
2. Go to your personal status page (should be at https://cms.sic.saarland/ct22/students/view ) and give preferences to topics via the tutorial preference selection mechanism. Each topic corresponds to one tutorial (except the "For auditing students" tutorial which you should ignore and give 0 points). Note that this assignment works by giving points to the topics / tutorials you do not want to lead. Input your preferences until the lecture this Friday (29.4.).
3. We will do the assignment of topics during the lecture on Friday 29.4.. Make sure to attend this lecture as we will assume that people not attending the lecture on 29.4. have dropped out of the course.

Please let us know if you have any questions.

Show all

Category Theory

Category theory is a relatively young branch of mathematics which provides a kind of "abstract theory of functions". It elucidates fundamental algebraic structures which have reappeared time and again throughout mathematics, computer science, and other disciplines, and it has proven particularly useful in organizing the foundations of logic, type theory, and programming languages. As such, anyone working on the more formal aspects of programming languages can benefit from an acquaintance with the basics of category theory.

In this seminar, we will work through an introductory textbook on category theory ("Category Theory" by Steve Awodey), covering such essential concepts as categories, functors, natural transformations, limits and colimits, functor categories, Yoneda's lemma, adjoints, and monads. Time permitting, we will also explore how category theory can be used in building the foundation of a modern, higher-order separation logic (Iris).

Requirements: An intermediate level of mathematical maturity is expected. Though there are no formal prerequisites, the course will be easiest to follow for students who have already taken Discrete Mathematics and Intro to Computational Logic (and/or Semantics).

Dates

The first session will be on Thursday 21.4. at 10:00 on Zoom (link can be found in the materials).

The following sessions will be on Fridays at 10:00 (s.t.) at the same Zoom link. In the future, some sessions might be in person.

Structure of the course

This course is structured around the book "Category Theory" by Steve Awodey. The idea is for students to read the chapter for the seminar session and try to solve the assigned exercises before each session. The session is then used to discuss any questions about the material and discuss the exercises. Each session will be led by a different student that gives a short presentation of the material, leads the discussion and afterwards hands in a solution of the homework exercises. Additionally, each session as an appointed scribe that will produce a summary of the discussion.

Concretely, each week is structured as follows:

Seminar session:

~15 minutes: The student in charge of the session briefly summarizes the most important concepts from the reading of the week. This presentation can assume that all participants have read the material and only need a quick refresher on it.
~30 minutes: The student in charge of the session initiates discussion about the chapter and any technical questions they have. Other students can also raise technical questions.
~45 minutes: The student in charge of the session goes over solutions to homework problems for the week.
(parts 2 and 3 above could be intermingled)
The appointed scribe for this session makes notes what is discussed.

Between sessions:

All students read the chapter corresponding to the next session from the Awodey book.
All students do the ~4 exercises associated with the reading for the next session.
The student in charge of the next session prepares to lead the next session (as described above).

Two weeks after a session:

The student in charge of the session hands in a write up of solutions to the homework problems.
The scribe of the session hands in a write up of "minutes" of the discussion and examples presented in class.

The leader of each session will be the scribe three weeks later (wrapping around the end of the semester).

Additional Material

This course follows the book "Category Theory" by Steve Awodey (available here), but it might be useful to consult other material for alternative explanations. Some suggestions can be found on the Materials page.

List of topics

Initial topics presented by the lecturers:

(21.4.) Categories 1 Ch. 1.1 - 1.4
(29.4.) Categories 2 Ch. 1.5, 1.6, 1.8

Student topics:

(6.5.) Abstract structures Ch. 2 Leader: Correnson, Arthur, Scribe: Mück, Niklas
(13.5.) Duality Ch. 3 Leader: Ramadoss, Nirmal Kumar, Scribe: Gautam, Vasundhara
(20.5.) Limits and colimits 1 Ch. 5.1 - 5.3 Leader: Hostert, Johannes, Scribe: Ye, Yuhan
(27.5.) Limits and colimits 2 Ch. 5.4 - 5.6 Leader: Jin, Jonathan, Scribe: Correnson, Arthur
(3.6.) Exponentials Ch. 6.1, 6.2, 6.5 - 6.6 Leader: Lohse, Janine, Scribe: Ramadoss, Nirmal Kumar
(10.6.) Naturality 1 Ch. 7.1, 7.2, 7.4, 7.5 Leader: Döring, Simon, Scribe: Husung, Nils
(17.6.) Naturality 2 Ch. 7.6 - 7.10 Leader: Baumann, Jonathan, Scribe: Jin, Jonathan
(24.6.) Categories of diagrams 1 Ch. 8.1 - 8.4 Leader: Husung, Nils, Scribe: Lohse, Janine
(1.7.) Categories of diagrams 2 Ch. 8.5 - 8.8 Leader: Peters, Benjamin, Scribe: Döring, Simon
(8.7.) Adjoints 1 Ch. 9.1 - 9.5 Leader: Mück, Niklas, Scribe: Peters, Benjamin
(15.7.) Adjoints 2 Ch. 9.6, 9.8 Leader: Gautam, Vasundhara, Scribe: Hostert, Johannes
(22.7.) Monads and algebras Ch. 10 Leader: Ye, Yuhan, Scribe: Baumann, Jonathan