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!
source & further reading
math.ucr.edu — original article