Learning Resources for Applied Category Theory

This post is a wiki post, so anyone can edit it! The purpose is to gather resources to help learn applied category theory. I will start with some basic resources, but I hope that other people add to this.

General Category Theory

Formal Mathematical Introductions

Informal Mathematical Introductions

Applied Introductions

Systems Theory

Learn Category Theory through Software

Related subjects

Sheaf Theory


Other resource lists


Shouldn’t the books list authors as well as titles? Usually people are interested in who wrote something. Unless there’s an objection, I could add some authors’ names.

Yes please! I also want to reiterate that this is meant to be edited; I would also encourage people to add summaries if they like particular resources.

Also I didn’t know about your course based on 7 sketches! That’s a fantastic resource.

Thanks! Simon Burton helped me transfer my lectures from the now-defunct Azimuth Forum to a self-standing set of web pages. It still needs to be polished in many ways, so bug reports would be helpful. I want to copy all the “puzzles” to these lectures.

I’ve been curating a similar list here!

I focused on very pedagogically oriented texts, so for instance CftWM is purposefully not there

Nice! I sort of knew that but sort of forgot it. It would be great if you could add

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I’ve added these:
Paolo Perrone, Notes on Category Theory
Ralph Sarkis, My First Category Theory Textbook

I’m wondering if these could also fit in this list, but I’m not sure:

By the way, I tend to download PDF copies of helpful resources, not just save links to them. This is because links tend to stop working after a few years - the address of the resource they intend to point to changes, or the site they point to stops existing. So, if we want this list to be useful for a long time, it might be worth considering options that could help mitigate this problem.


That’s a good idea! Do you want to start a github repository with pdfs from this list, and then add links in this list to the pdfs in the repository along with the original source?

I like the idea of starting a github repository with pdfs from this list! While I personally don’t want to take on the work of maintaining such a repository right now, perhaps there is someone else who would be interested in doing so.

By the way, my Lectures on Applied Category Theory will keep changing as I fix them up. So while a github repository of PDFs is a good way of getting a snapshot in time, that has its bad sides as well as its (more important) good sides.

I alphabetized resources within sections by last name, is that okay?

@owenlynch , @DavidEgolf I would also volunteer to start a github repository with pdf links to most (not @johncarlosbaez 's and other dynamically evolving resources), once I learn how to do such a thing. Would it be a repository in the LocalCharts github?

Why don’t we just put those in the forest, in the assets/ folder? Then we could make references for each of them with proper bibliographic information as well.

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