Please enable JavaScript
Applied Category Theory CourseApplied Category Theory Course
John Baez
This is a course based on Fong and Spivak's book<br>Seven Sketches in Compositionality: An Invitation to Applied Category Theory,<br>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!
© 2018 John Baez