Intermediate category theory reading group
When?
2025–2026 Semester 1. One two-hour meeting per week, each Wednesday 15:00–17:00.
Update: the 2025-11-05 meeting has been moved to Thursday 2025-11-06, 10:00–12:00, to avoid a clash with the CDT conference.
Where?
Bayes Centre 4.45 (Edinburgh), other than 2025-11-19 when we’ll be in 3.56; and Advanced Research Centre room 376 (Glasgow), connected together via video call. Always hybrid online anyway: please join the Zulip chat to get the video call links.
Update: rooms for 2025-11-06 TBC. Same video call details as usual.
What?
For the first part of this reading group, we will cover Chapter 5, monads; and Chapter 6, Kan extensions; of Emily Riehl’s book Category Theory in Context. Monads are beautiful mathematical objects that can describe algebraic theories, computational effects, and various other mathematical phenomena. Kan extensions give a powerful approach for generalising many category theoretic constructions – the saying goes that ‘everything is Kan extensions’! Then, we will switch to a more free-form approach: this might include presentations by participants on topics, papers, or general ideas of interest. I expect that topoi or enriched categories (likely including higher categories) may make an appearance.
Please see the syllabus from the proposal for this reading group (82KB) for more information, including prerequisites.
The primary group organiser is me, Maia Woolf (she/her), and you can contact me via email to maia.woolf@ed.ac.uk. Discussion about the course will (outside of the group meetings) primarily happen in the group Zulip chat. Please send me an email if you have not already been given the link to the chat and would like to join.
Schedule
The rough schedule for each week is as follows. The numbers such as 5.1 refer to the sections in the book. Many thanks to all speakers and notetakers!
| Week | Date | Topic | Speaker | Notetaker |
|---|---|---|---|---|
| 1 | 2025-10-08 | Recap of prerequisites | Maia Woolf | Jack Heaney – notes (377KB) |
| 2 | 2025-10-15 | Monads: 5.1–5.2 | Maia Woolf | Maia Woolf (backup) – notes (48KB) |
| 3 | 2025-10-22 | Monads: 5.3–5.4 | Nikolai Stor | Willoughby Seago – notes (2554KB) |
| 4 | 2025-10-29 | Monads: 5.5–5.6 | Willoughby Seago – speaker’s notes (3804KB) | Nikolai Stor – notes (8967KB) |
| 5 | Exceptionally 2025-11-06, 10:00–12:00 | Kan extensions: 6.1–6.2 | Cassia Edwards | Maia Woolf |
| 6 | 2025-11-12 | Kan extensions: 6.3–6.5 | Jack Heaney | |
| 7 | 2025-11-19 (Bayes in 3.56) | Context overflow/recap/presented topic | Jack Heaney | |
| 8 | 2025-11-26 | Presented topic | Emmanouil Sfinarolakis | |
| 9 | 2025-12-03 | Presented topic | Cassia Edwards | |
| 10 | 2025-12-10 | Presented topic |