几年前， 遇到一个文科生的神人。 他问我面向对象是什么， 我说是一种抽象，给他讲了一大堆， 类， 继承，多态之类的概念。
最后他若有所思， 原来你说的就是分类啊。 他这个回复把震惊了，原来一直都没有搞懂真相的是我， 事实上还真的就是分类的方法。

这几年我才看到有一门问叫 Category Theory ， 原来这玩意儿可以搞的这么高深。

https://math.ucr.edu/home/baez/act_course/index.html…

Applied Category Theory Course

Source: https://math.ucr.edu/home/baez/act_course/index.html Applied Category Theory CourseJohn 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!

© 2018 John Baez