Lectures on Applied Category Theory
Posted by John Baez
Want to learn applied category theory? You can now read my lectures here:
There are a lot, but each one is bite-sized and basically covers just one idea. They’re self-contained, but you can also read them along with Fong and Spivak’s free book to get two outlooks on the same material:
- Brendan Fong and David Spivak, Seven Sketches in Compositionality: An Invitation to Applied Category Theory.
Huge thanks go to Simon Burton for making my lectures into nice web pages! But they still need work. If you see problems, please let me know.
Here’s one problem: I need to include more of my ‘Puzzles’ in these lectures. None of the links to puzzles work. Students in the original course also wrote up answers to all of these puzzles, and to many of Fong and Spivak’s exercises. But it would take quite a bit of work to put all those into webpage form, so I can’t promise to do that. 😢
Here are the lectures:
Chapter 1: Ordered Sets
-
Lecture 1 - Introduction
-
Lecture 2 - What is Applied Category Theory?
-
Lecture 3 - Preorders
-
Lecture 4 - Galois Connections
-
Lecture 5 - Galois Connections
-
Lecture 6 - Computing Adjoints
-
Lecture 7 - Logic
-
Lecture 8 - The Logic of Subsets
-
Lecture 9 - Adjoints and the Logic of Subsets
-
Lecture 10 - The Logic of Partitions
-
Lecture 11 - The Poset of Partitions
-
Lecture 12 - Generative Effects
-
Lecture 13 - Pulling Back Partitions
-
Lecture 14 - Adjoints, Joins and Meets
-
Lecture 15 - Preserving Joins and Meets
-
Lecture 16 - The Adjoint Functor Theorem for Posets
-
Lecture 17 - The Grand Synthesis
Chapter 2: Resource Theories
-
Lecture 18 - Resource Theories
-
Lecture 19 - Chemistry and Scheduling
-
Lecture 20 - Manufacturing
-
Lecture 21 - Monoidal Preorders
-
Lecture 22 - Symmetric Monoidal Preorders
-
Lecture 23 - Commutative Monoidal Posets
-
Lecture 24 - Pricing Resources
-
Lecture 25 - Reaction Networks
-
Lecture 26 - Monoidal Monotones
-
Lecture 27 - Adjoints of Monoidal Monotones
-
Lecture 28 - Ignoring Externalities
-
Lecture 29 - Enriched Categories
-
Lecture 30 - Preorders as Enriched Categories
-
Lecture 31 - Lawvere Metric Spaces
-
Lecture 32 - Enriched Functors
-
Lecture 33 - Tying Up Loose Ends
Chapter 3: Databases
-
Lecture 34 - Categories
-
Lecture 35 - Categories versus Preorders
-
Lecture 36 - Categories from Graphs
-
Lecture 37 - Presentations of Categories
-
Lecture 38 - Functors
-
Lecture 39 - Databases
-
Lecture 40 - Relations
-
Lecture 41 - Composing Functors
-
Lecture 42 - Transforming Databases
-
Lecture 43 - Natural Transformations
-
Lecture 44 - Categories, Functors and Natural Transformations
-
Lecture 45 - Composing Natural Transformations
-
Lecture 46 - Isomorphisms
-
Lecture 47 - Adjoint Functors
-
Lecture 48 - Adjoint Functors
-
Lecture 49 - Kan Extensions
-
Lecture 50 - Left Kan Extensions
-
Lecture 51 - Right Kan Extensions
-
Lecture 52 - The Hom-Functor
-
Lecture 53 - Free and Forgetful Functors
-
Lecture 54 - Tying Up Loose Ends
Chapter 4: Collaborative Design
-
Lecture 55 - Enriched Profunctors and Collaborative Design
-
Lecture 56 - Feasibility Relations
-
Lecture 57 - Feasibility Relations
-
Lecture 58 - Composing Feasibility Relations
-
Lecture 59 - Cost-Enriched Profunctors
-
Lecture 60 - Closed Monoidal Preorders
-
Lecture 61 - Closed Monoidal Preorders
-
Lecture 62 - Enriched Profunctors
-
Lecture 63 - Composing Enriched Profunctors
-
Lecture 64 - The Category of Enriched Profunctors
-
Lecture 65 - Collaborative Design
-
Lecture 66 - Collaborative Design
-
Lecture 67 - Feedback in Collaborative Design
-
Lecture 68 - Feedback in Collaborative Design
-
Lecture 69 - Feedback in Collaborative Design
-
Lecture 70 - Tensoring Enriched Profunctors
-
Lecture 71 - Caps and Cups for Enriched Profunctors
-
Lecture 72 - Monoidal Categories
-
Lecture 73 - String Diagrams and Strictification
-
Lecture 74 - Compact Closed Categories
-
Lecture 75 - The Grand Synthesis
-
Lecture 76 - The Grand Synthesis
-
Lecture 77 - The End? No, the Beginning!
Links to puzzles
John, the links to the puzzles in Lecture 3 don’t seem to be working for me after trying a couple of browsers.