Category Theory : Motivation and Philosophy

Math Online Tom Circle

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”…

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About tomcircle

Math amateur
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