Category Theory 25

Info. 10(-11?) lectures of 90 minutes each. Course period covers the first half of the second semester of 2025. Meeting once a week. The lectures will be delivered at Humanisten, every Tuesday from 13.15 to 15.15 o'clock. We start the 21st of January. The room may change from time to time, we start in J577 room

Lectures are decorated by additional material. Click on the for an exercise sheet that will help you to familiarise with the subject, this document also contains a very synthetic summary of the lecture. Check out for some lecture notes, and for a pre-recorded video of the lecture. Finally, the will open one of the two graded homework. Notice that the exercise sheets are not graded and completely optional, they are meant to offer a playground to familiarise with the topic.


Title Material Reference
1. Categories, functors, natural transformations. Lei, Chap. 1.
2. Limits, colimits, monos and epis. Lei, Chap. 5.
3. Adjunctions. Lei, Chap. 2.
4. Prolegomena ad Yoneda: Posets.
5. Yoneda: Presheaves, representability, embedding. Lei, Chap. 4.
6. Interactions: Yoneda, adjunctions and limits. Lei, Chap. 6.
7. Prolegomena ad Monads and Kan: Posets.
8. Monads. Rie, Chap. 5.
9. Kan Extensions (and adjoint functor theorem). Rie, Chap. 6.
10. Monoidal (closed) categories and enrichments. Chap. 3.

Audience. The course is open to bachelor and master students. The audience is expected to have attended (the equivalent of) an introductory course in at least two of the following topics: general topology, algebraic topology, group theory, module theory, universal algebra, model theory.

Syllabus. Categories, functors, natural transformations. Limits and Colimits. Adjunctions. Toy Category Theory: posets. Yoneda: Presheaves, representability, Yoneda embedding. Monads. Kan extentions. Towards enriched categories: monoidal (closed) categories and enrichments.

Exam. The exam comprises of two homework () (25%+25%) and an oral examination (50%). Each of these three parts of the exam is graded from 1 to 10. The student's final mark will be U is the weighted mean is strictly below 5, G if the weighted mean is between 5 and 7, VG if the weighted mean is strictly above 7.

Bibliography.

In my personal experience, Category theory has proven to be a seductive and dangerous field, especially for youngsters. Please avoid the Scuttle paradox.