This is the category theory section of the undergraduate seminar MATHUN3952. Please reach out to me with any questions at ca3172 (at) columbia (dot) edu.
We will generally follow Emily Riehl's book "Category Theory in Context" but feel free to let me know if there is a related topic you'd prefer to present on.
You can reach me by email to schedule a meeting before your talk if you'd like, and also please let me know if I have miswritten your name or if there is another name
you would prefer that I write on the schedule.
Meeting Time and Location: Tuesdays (HAM406)/Thursdays(HAM408) 4:40pm-5:40pm
Course Policy Reminders: Students are expected to attend all meetings and absences must be excused beforehand. Each participant will give 1 or 2 talks over the course of the semester.
Section Policy: Your grade may be impacted after 25% or more unexcused absences. We will only allow chalk talks and you may not use AI to help prepare your talk.
1. Introduction
Carlos Andrés Alvarado Álvarez 02/03/26
We will go over general course policy and assign talks for the first weeks. With the remaining time we'll introduce some basic concepts in category theory.
2. Algebra
Carlos Andrés Alvarado Álvarez 02/05/26
We will introduce some basic concepts in abstract algebra as these provide many examples of categories and can help illustrate a lot of key ideas.
3. Categories and Functors
Younggi Daniel Moon 02/10/26
Sections 1.1, 1.2 and 1.3. Notes available here.
4. Naturality
Kathy Xu 02/12/26
Sections 1.4, 1.5 and 1.6
5. Yoneda Lemma
Zara Tse 02/17/26
Sections 2.1 and 2.2
6. Universal Properties
Sarah Hong 02/19/26
7. (co)limits I
Donghan Fan 02/24/26
8. (co)limits II
Joseph McGill 02/26/26
Sections 3.4, 3.5 and 3.6
9. (co)limits III
Maira Molina 03/03/26
Sections 3.2, 3.3
10. (co)limits IV
Samantha Swerdlin Katz 03/05/26
Sections 3.8 + review
11. Adjunctions I
Seung Jae Hong 03/10/26
Sections 4.1 + Econ
12. Adjunctions II
Cynthia Fu 03/12/26
Sections 4.1 and 4.2
13. Adjunctions III
Seung Jae Hong 03/24/26
Sections 4.3 and 4.4
14. Adjunctions IV
Kathy Xu 03/26/26
Sections 4.5
15. Adjunctions IV
tbd 03/31/26
Sections 4.6
16. Adjunctions V
tbd 04/02/26
Review of adjunctions