Applied Category Theory Course (2018)

John Baez taught an online course on applied category theory based on Fong and Spivak's book 'Seven Sketches in Compositionality', with webpages created by Simon Burton. The course covered ordered sets, resource theories, databases, and collaborative design through 64 lectures.

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 lecture 1.html - Introduction - Lecture 2 lecture 2.html - What is Applied Category Theory? - Lecture 3 lecture 3.html - Preorders - Lecture 4 lecture 4.html - Galois Connections - Lecture 5 lecture 5.html - Galois Connections - Lecture 6 lecture 6.html - Computing Adjoints - Lecture 7 lecture 7.html - Logic - Lecture 8 lecture 8.html - The Logic of Subsets - Lecture 9 lecture 9.html - Adjoints and the Logic of Subsets - Lecture 10 lecture 10.html - The Logic of Partitions - Lecture 11 lecture 11.html - The Poset of Partitions - Lecture 12 lecture 12.html - Generative Effects - Lecture 13 lecture 13.html - Pulling Back Partitions - Lecture 14 lecture 14.html - Adjoints, Joins and Meets - Lecture 15 lecture 15.html - Preserving Joins and Meets - Lecture 16 lecture 16.html - The Adjoint Functor Theorem for Posets - Lecture 17 lecture 17.html - The Grand Synthesis Chapter 2: Resource Theories - Lecture 18 lecture 18.html - Resource Theories - Lecture 19 lecture 19.html - Chemistry and Scheduling - Lecture 20 lecture 20.html - Manufacturing - Lecture 21 lecture 21.html - Monoidal Preorders - Lecture 22 lecture 22.html - Symmetric Monoidal Preorders - Lecture 23 lecture 23.html - Commutative Monoidal Posets - Lecture 24 lecture 24.html - Pricing Resources - Lecture 25 lecture 25.html - Reaction Networks - Lecture 26 lecture 26.html - Monoidal Monotones - Lecture 27 lecture 27.html - Adjoints of Monoidal Monotones - Lecture 28 lecture 28.html - Ignoring Externalities - Lecture 29 lecture 29.html - Enriched Categories - Lecture 30 lecture 30.html - Preorders as Enriched Categories - Lecture 31 lecture 31.html - Lawvere Metric Spaces - Lecture 32 lecture 32.html - Enriched Functors - Lecture 33 lecture 33.html - Tying Up Loose Ends Chapter 3: Databases - Lecture 34 lecture 34.html - Categories - Lecture 35 lecture 35.html - Categories versus Preorders - Lecture 36 lecture 36.html - Categories from Graphs - Lecture 37 lecture 37.html - Presentations of Categories - Lecture 38 lecture 38.html - Functors - Lecture 39 lecture 39.html - Databases - Lecture 40 lecture 40.html - Relations - Lecture 41 lecture 41.html - Composing Functors - Lecture 42 lecture 42.html - Transforming Databases - Lecture 43 lecture 43.html - Natural Transformations - Lecture 44 lecture 44.html - Categories, Functors and Natural Transformations - Lecture 45 lecture 45.html - Composing Natural Transformations - Lecture 46 lecture 46.html - Isomorphisms - Lecture 47 lecture 47.html - Adjoint Functors - Lecture 48 lecture 48.html - Adjoint Functors - Lecture 49 lecture 49.html - Kan Extensions - Lecture 50 lecture 50.html - Left Kan Extensions - Lecture 51 lecture 51.html - Right Kan Extensions - Lecture 52 lecture 52.html - The Hom-Functor - Lecture 53 lecture 53.html - Free and Forgetful Functors - Lecture 54 lecture 54.html - Tying Up Loose Ends Chapter 4: Collaborative Design - Lecture 55 lecture 55.html - Enriched Profunctors and Collaborative Design - Lecture 56 lecture 56.html - Feasibility Relations - Lecture 57 lecture 57.html - Feasibility Relations - Lecture 58 lecture 58.html - Composing Feasibility Relations - Lecture 59 lecture 59.html - Cost-Enriched Profunctors - Lecture 60 lecture 60.html - Closed Monoidal Preorders - Lecture 61 lecture 61.html - Closed Monoidal Preorders - Lecture 62 lecture 62.html - Enriched Profunctors - Lecture 63 lecture 63.html - Composing Enriched Profunctors - Lecture 64 lecture 64.html - The Category of Enriched Profunctors - Lecture 65 lecture 65.html - Collaborative Design - Lecture 66 lecture 66.html - Collaborative Design - Lecture 67 lecture 67.html - Feedback in Collaborative Design - Lecture 68 lecture 68.html - Feedback in Collaborative Design - Lecture 69 lecture 69.html - Feedback in Collaborative Design - Lecture 70 lecture 70.html - Tensoring Enriched Profunctors - Lecture 71 lecture 71.html - Caps and Cups for Enriched Profunctors - Lecture 72 lecture 72.html - Monoidal Categories - Lecture 73 lecture 73.html - String Diagrams and Strictification - Lecture 74 lecture 74.html - Compact Closed Categories - Lecture 75 lecture 75.html - The Grand Synthesis - Lecture 76 lecture 76.html - The Grand Synthesis - Lecture 77 lecture 77.html - The End? No, the Beginning