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