# The Azimuth Project Applied Category Theory Course (changes)

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# Contents

## Idea

From May until September 2018, John Baez taught a free online course called Applied Category Theory . The lectures and exercises from that course are available here. Starting in January 2019 there will be anApplied Category Theory Seminar at U.C. Riverside, which will also be available online. Click for details!

The course was based on this book:

It’s 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. 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:

Also, starting in January 2019 there be an Applied Category Theory Seminar at U.C. Riverside, available online. Click for details!

Here is the course material:

## 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.

To read and join discussions on Chapter 4 go here:

You can also do Exercises and puzzles.

## 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:

### Errata

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

By John Baez:

By others:

### Wiki Pages

Candidates for becoming wiki pages include:

### Just for Fun

These are fun digressions:

category: courses