A lot happened at Applied Category Theory 2018. Even as it’s still winding down, we’re already starting to plan a followup in 2019, to be held in Oxford. Here are some notes Joshua Tan sent out:

Discussions: Minutes from the discussions can be found here.

Photos: Ross Duncan took some very glamorous photos of the conference, which you can find here.

Videos: Videos of talks are online here: courtesy of Jelle Herold and Fabrizio Genovese.

Next year’s workshop: Bob Coecke will be organizing ACT 2019, to be hosted in Oxford sometime spring/summer. There will be a call for papers.

Next year’s school: Daniel Cicala is helping organize next year’s ACT school. Please contact him at if you would like to get involved.

Look forward to the official call for submissions, coming soon, for the first issue of Compositionality!

The minutes mentioned above contain interesting thoughts on these topics:

• Day 1: Causality
• Day 2: AI & Cognition
• Day 3: Dynamical Systems
• Day 4: Systems Biology
• Day 5: Closing

I looked at the Category Theory course and I was upset, I don’t know why, and on reflection I still don’t know why. Category Theory is a generalisation, not a set of examples. It is an overarching theory that itself needs generalisation. Above all, everything needs proofs. I agree examples have to come first. This provides meaning to generalisations. But here we start with complicated definitions with no motivation, and then give examples which fit. This is not right. I can’t wade through this jungle. The overarching idea is simple. Simplicity must be retained. From the simple we descend methodically or by interest to the complicated. I don’t agree that mathematics is about solving set problems with known solutions anyway. If problems are interesting, they may lead to abstract theory and this is OK. The purpose of university is not to do exercises, but to understand overarching ideas. Exercises, if too much time is spent on them, detract from the study of what mathematics is, its major problems, and what it is about. This is important, not exercises, and definitely not the social accreditation that goes with the accumulation of marks. I actually think I disagree with some theorems you give. I have not proved any of this, but it is part of my approach in the still very much unfinished Number, Space and Logic, which will be 1,000 pages, gives an overview of all mathematics, and extends its scope, language and structure considerably.

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I looked at the Category Theory course and I was upset, I don’t know why, and on reflection I still don’t know why. Category Theory is a generalisation, not a set of examples. It is an overarching theory that itself needs generalisation. Above all, everything needs proofs. I agree examples have to come first. This provides meaning to generalisations. But here we start with complicated definitions with no motivation, and then give examples which fit. This is not right. I can’t wade through this jungle. The overarching idea is simple. Simplicity must be retained. From the simple we descend methodically or by interest to the complicated. I don’t agree that mathematics is about solving set problems with known solutions anyway. If problems are interesting, they may lead to abstract theory and this is OK. The purpose of university is not to do exercises, but to understand overarching ideas. Exercises, if too much time is spent on them, detract from the study of what mathematics is, its major problems, and what it is about. This is important, not exercises, and definitely not the social accreditation that goes with the accumulation of marks. I actually think I disagree with some theorems you give. I have not proved any of this, but it is part of my approach in the still very much unfinished Number, Space and Logic, which will be 1,000 pages, gives an overview of all mathematics, and extends its scope, language and structure considerably.

Jim H Adams