Applied Category Theory

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

- Brendan Fong and David Spivak,
*Seven Sketches in Compositionality.*

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:

Start the course here:

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:

- Lecture 3 - Chapter 1: Preorders
- Lecture 4 - Chapter 1: Galois Connections
- Lecture 5 - Chapter 1: Galois Connections
- Lecture 6 - Chapter 1: Computing Adjoints
- Lecture 7 - Chapter 1: Logic
- Lecture 8 - Chapter 1: The Logic of Subsets
- Lecture 9 - Chapter 1: Adjoints and the Logic of Subsets
- Lecture 10 - Chapter 1: The Logic of Partitions
- Lecture 11 - Chapter 1: The Poset of Partitions
- Lecture 12 - Chapter 1: Generative Effects
- Lecture 13 - Chapter 1: Pulling Back Partitions
- Lecture 14 - Chapter 1: Adjoints, Joins and Meets
- Lecture 15 - Chapter 1: Preserving Joins and Meets
- Lecture 16 - Chapter 1: The Adjoint Functor Theorem for Posets
- Lecture 17 - Chapter 1: The Grand Synthesis

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 are created by class members.

Applied Category Theory - Chapter 1 - Puzzles

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

Applied Category Theory - Sketch 2 - Exercises and Puzzles

For information on how the Azimuth Forum works, see:

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

By John Baez:

By others:

Candidates for becoming wiki pages include:

These are fun digressions: