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:

You can also do Exercises and Puzzles. 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 2 go here:

You can also do Exercises and puzzles. Here are the lectures on Chapter 2:

Chapter 3: Databases

Chapter 3 is about databases - and now we will finally meet categories, functors, adjoint functors, and Kan extensions.

To read and join discussions on Chapter 3 go here:

You can also do Exercises and puzzles. Here are the lectures on Chapter 3:

Chapter 4: Collaborative Design

Chapter 4 is about collaborative design, and how we can use enriched profunctors to relate resources to requirements.

Puzzles

Puzzles are created by class members.

Exercises

Here are the exercises from the book, often with solutions:

Course Materials

For information on how the Azimuth Forum works, see:

GitBook version of Course Lectures

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:

category: courses