Category Theory : Motivation and Philosophy

Object-Oriented has 2 weaknesses for Concurrency and Parallel programming :

1. Hidden Mutating States;
2. Data Sharing.

Category Theory (CT): a higher abstraction of all different Math structures : Set , Logic, Computing math, Algebra… =>

$latex boxed {text {CT reveals the way how our brain works by analysing, reasoning about structures
!}}&fg=aa0000&s=3$

Our brain works by: 1) Abstraction 2) Composition 3) Identity (to identify)

What is a Category ?
1) Abstraction:

• Objects
• Morphism (Arrow)

2) Composition: Associative
3) Identity

Notes:

• Small Category with “Set” as object.
• Large Category without Set as object.
• Morphism is a Set : “Hom” Set.

Example in Programming:

• Object : Types Set
• Morphism : Function “Sin” converts degree to R: $latex sin frac {pi}{2} = 1$

Note: We just look at the Category “Types Set” from external Macroview, “forget ” what it contains, we only know the “composition” (Arrows) between the Category “Type Set”, also “forget”…