Category Theory 20

Info. Every Tuesday from 15 to 17 o'clock. We start the 6th of October.
The course will completely be on Zoom. Click here to attend the lectures. The password is 728002. If you send me an email about this course make sure to include the word CT20 in the subject. This makes my life easier.

Lectures are decorated by additional material. Click on the for the exercise sheet and a very synthetic summary of the lecture. Check out for the lecture notes, and finally redirects to the footage of the lecture.

	Title	Material	Reference
1.	Categories, functors, natural transformations.		Lei, Chap. 1.
2.	Limits, colimits, monomorphisms and epimorphisms.		Lei, Chap. 5.
3.	Adjunctions.		Lei, Chap. 2.
4.	Prolegomena ad Yoneda: Posets.
5.	Yoneda: Presheaves, representability, embedding.		Lei, Chap. 4.
6.	Interactions between 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.

Audience. The course is open to bachelor, master students and researchers that are not familiar with the topic. The audience is expected to have attended 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.

Exercises. For every lesson we will provide an exercise sheet. Given that this course does not provide credits, they are not mandatory. Though, I indicate in the exercise sheet a suggested amount of exercises and I am happy to correct and discuss the exercises with the students.

Bibliography.

Basic Category Theory by Tom Leinster.
Category Theory in Context by Emily Riehl.
Handbook of categorical algebra, Vol. I & II by Francis Borceux.
Further readings.

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