Applied Category Theory Seminar
WiSe 2025 Uni Greifswald

This is teaching material for the course "Kategorientheorie in den Naturwissenschaften" (Category Theory in the Natural Sciences).

For further details check out the syllabus.

Background Material and References

We first focus on basic categorical concepts (such as categories, functors, natural transformation). Here are some good sources:

1. S. Mac Lane, Categories for the working mathematician, second edition, Graduate Texts in Mathematics, 5, Springer, New York, 1998
2. E. Riehl, Category theory in context, Aurora Dover Modern Math Originals, Dover, Mineola, NY, 2016, available online
3. T. Leinster, Basic Category Theory, Cambridge Studies in Advanced Mathematics, 143, Cambridge Univ. Press, Cambridge, 2014, available online
4. M. Brandenburg, Einführung in die Kategorientheorie. Mit ausführlichen Erklärungen und zahlreichen Beispielen, 2nd revised edition. Heidelberg: Springer Spektrum, 2017

There are also some good resources on category theory from an applied perspective:

1. B. Fong, D. I. Spivak, Seven Sketches in Compositionality: An Invitation to Applied Category Theory, available online
2. J. Baez, Applied Category Theory Course, lecture notes available online

Talk Topics

Every student should pick a subject based on the list in the syllabus and prepare a talk addressing four questions:

1. Background material related to the application.
2. Relevant categorical background.
3. How category theory is applied in this particular context.
4. Whether the categorical application is in fact useful.

Further Links

Here are further links that can be helpful:

1. The Adjoint School has a lot of relevant content.
2. The Awesome Applied Category Theory contains many useful resources.
3. The Category Theory Zulip contains a lot of useful content and interesting discussions.