Tangent Categories Mini-Course
13–16 October 2026. Livingstone Tower, Department of Computer and Information Sciences, University of Strathclyde.
Programme
Tuesday 13th October (LT309)
| Time | Lecture |
|---|---|
| 09:00–09:30 | Registration and coffee |
| 09:30–10:30 | Tangent categories lecture 1 (video) Geoffrey Cruttwell |
| 10:30–11:00 | Coffee break |
| 11:00–12:00 | Containers lecture 1 (video) Robert Atkey |
| 12:00–14:00 | Lunch |
| 14:00–15:00 | Tangent categories lecture 2 (video) Geoffrey Cruttwell |
Wednesday 14th October (LT307)
| Time | Lecture |
|---|---|
| 10:00–11:00 | Containers lecture 2 (video) Robert Atkey |
| 11:00–11:30 | Coffee break |
| 11:30–12:30 | Tangent categories lecture 3 (video) Geoffrey Cruttwell |
| 12:30–14:30 | Lunch |
| 14:30–15:30 | Tangent categories lecture 4 (video) Geoffrey Cruttwell |
Friday 16th October (LT210)
| Time | Lecture |
|---|---|
| 11:00–12:00 | Tangent categories lecture 5 (video) Geoffrey Cruttwell |
| 12:00–14:00 | Lunch |
| 14:00–15:00 | Containers lecture 3 (video) Conor Titania McBride |
| 15:00–15:30 | Coffee break |
| 15:30–16:30 | Tangent categories lecture 6 (video) Geoffrey Cruttwell |
| 17:00 | Pub |
Courses
Tangent categories tutorial (Geoffrey Cruttwell, Mount Allison University)
Abstract: Tangent categories are a "minimal" categorical setting for differential geometry. Previous work on categorical machine learning has used cartesian differential categories (and variants of it), but that abstraction is not flexible enough to work with learning on manifolds. Tangent categories enable one to "do differential geometry" on manifolds and many other settings, and thus represent the "next step" for the study of categorical machine learning.
In this tutorial I'll introduce what tangent categories are, give a variety of models for their axioms, and show some of their theory. Basic category theory knowledge is assumed, but I will not assume any knowledge of differential geometry or categorical machine learning.
Containers: Theory and Applications (Robert Atkey and Conor Titania McBride, University of Strathclyde)
Unfortunately the original lecturers had to cancel at the last minute. Fortunately Robert Atkey and Conor Titania McBride have kindly accepted the invitation to give a course on containers to make up for this.
Original course details
Lecturers: Neil Ghani and Orestis Melkonian, Kodamai.
Abstract: A container is a strikingly simple idea: a set of prompts, and for each prompt a set of admissible responses. From this modest starting point comes an enormous range of structure — every ordinary data type arises as the least fixed point of a container, and the functors they denote, the polynomial functors, sit at the heart of type theory, category theory, and functional programming. A container is at once a data type and a typed interface, specifying for every prompt exactly which responses are valid, and it carries a rich algebra: several monoidal structures, a well-behaved notion of morphism, closed structure, and a derivative.
This series introduces containers from the ground up, and then follows them into computer science. We cover the basic theory — the definition and its readings, the extension to polynomial functors, container morphisms, the monoidal and closed structures, free and cofree containers, monads over containers, and indexed and directed containers — before turning to applications: machine learning, agentic AI, theorem proving, and differential algebra.
Registration
Registration has now closed. Attendance is free, but participants needed to register for planning purposes.
Venue
The lectures will take place in Livingstone Tower, which is part of the University of Strathclyde. Livingstone Tower is in central Glasgow, near to both Glasgow Queen Street station and Glasgow Central Station.
There will be signs from the entrance of Livingstone Tower each day.
Livestream and recordings
We will do our best to livestream and record the lectures. Obviously if you would like to interact with the lecturers by asking questions, etc, in-person attendance is strongly recommended.
The livestream will be available here: https://www.youtube.com/@msp.strathclyde/streams with recordings collected in a playlist.