Applied Category Theory Course

John Baez

This is a course based on Fong and Spivak's book Seven Sketches in Compositionality: An Invitation to Applied Category Theory, taught by John Baez and turned into nice webpages by Simon Burton.

For more details, dive right in and check out Lecture 1.

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!