Category Theory III for Programmers (Parts 1 & 2)

The most interesting “Category Theory” （范畴论) for Programmers course III by Dr. Bartosz Milewski , a follow-up of last year’s course II.

Prerequisites:

1. Fundamental of Category Theory: Functor, Natural Transformation, etc. (Course II Series)
2. (Nice to have) : Basic Haskell Functional Programming Language. (Quick Haskell Tutorial)

1.1: Overview Part 1

Category Theory (CT) = Summary ofALL Mathematics

Functional Programming = Application of CT

Philosophical Background:

• Math originated 3,000 years ago in Geometry by Greek Euclid with Axioms and deductive （演译） Proof-drivenLogic.
• Geometry = Geo (Earth) + Metry (Measurement).
• Math evolved from 2-dimensional Euclidean Geometry through 17 CE French Descartes’s Cartesian Geometry using the 13CE Arabic invention “Algebra” in Equations of n dimensions: $latex (x_1, x_2,…, x_n) $, $latex (y_1, y_2,…, y_n) $
• Use of Algebra: 1) Evaluation of algebraic equations (in CT: “Functor”) ; 2) Manipulation. eg. Substitution (in CT :…