Successfully reported this slideshow.

# Category Theory in 10 Minutes

Upcoming SlideShare
×

# Category Theory in 10 Minutes

A 10 minute lightning talk that highlights the 3 most important aspects of Category Theory as it relates to Functional Programming.

A 10 minute lightning talk that highlights the 3 most important aspects of Category Theory as it relates to Functional Programming.

## More Related Content

### Category Theory in 10 Minutes

1. 1. Category Theory in 10 Minutes Jordan Parmer @ProfParmer
2. 2. What’s Category Theory?
3. 3. What’s Category Theory? Mathematical study of abstract algebras of functions Systems of functions among some objects
4. 4. What’s a Category?
5. 5. A B f
6. 6. A B fObject Object Arrow/Morphism
7. 7. A B fObject Arrow/Morphism Object Domain (f) Codomain (f)
8. 8. A B C f g
9. 9. A B C f g g ∘ f g ∘ f = g ( f ( a ) )
10. 10. A B C f g g ∘ f Object domain(f) Arrow Composite Object codomain(f) domain(g) Arrow Object codomain(g)( g ◦ f )( a ) = g ( f ( a ) ) a ∈ A
11. 11. A B C f g g ∘ f ● Unit (identity) law: 1A : A → A, f ∘ 1A = f = 1B ∘ f ● Associativity law: h ∘ (g ∘ f) = (h ∘ g) ∘ f
12. 12. A B C h g g ∘ f D f h ∘ g
13. 13. Category theory is just mathematicians playing Portal.
14. 14. Oh the names we’ll use... Category theory is comprised of many small, simple laws. Adding a certain combination of laws together forms various algebraic structures each with their own name.