https://math.ucr.edu/home/baez/act_course/ Please enable JavaScript 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! --------------------------------------------------------------------- (c) 2018 John Baez