The Azimuth Project
Applied Category Theory

Contents

Idea

Applied Category Theory is an online course being taught by John Baez based on this free book:

It’s an invitation to advanced topics in category theory through concrete, real-world examples. It aims to give a tour: a gentle, quick introduction to guide later exploration. The tour takes place over seven sketches, each pairing an evocative application, such as databases, electric circuits, or dynamical systems, with the exploration of a categorical structure, such as adjoint functors, enriched categories, or toposes. No prior knowledge of category theory is assumed.

The primary purpose of this page is to help you navigate the course, which is being held in the Applied Category Theory Course section of the Azimuth Forum. For a quick overview, try this:

The Course

Start the course here:

Chapter 1: Ordered Sets

The motivation for choosing preorders as our first kind of category for study is to illustrate “generative effects”. To read and join discussions on Chapter 1 go here:

Here are the lectures on Chapter 1:

Chapter 2: Resource Theories

Chapter 2 is about resource theories. These allow us to tackle questions like:

  • Given what I have, is it possible to get what I want?
  • Given what I have, what is the minimum cost to get what I want?
  • Given what I have, what is the set of ways to get what I want?

The technical tools you’ll learn in this chapter include string diagrams, monoidal preorders and enrichment. To read and join discussions on Chapter 1 go here:

Here are the lectures on Chapter 2:

Puzzles

Puzzles are created by class members.

Applied Category Theory - Chapter 1 - Puzzles

Exercises

Exercises are taken from the text. Please add links to “exercise” pages on the forum, like these:

Chapter 1

Chapter 2

Applied Category Theory - Sketch 2 - Exercises and Puzzles

Course Materials

For information on how the Azimuth Forum works, see:

Errata

A discussion was started but the proper place to record and track errors in the text is here.

Other Materials

By John Baez:

By others:

Wiki Pages

Candidates for becoming wiki pages include:

Just for Fun

These are fun digressions: