A very basic introductory presentation on Category Theory. Focus was on directly relating category theory to programming in a functional language. Scala was the language of choice for the presentation. Basic coverage of Functors. Monads to follow in later talk.

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Category Theory for Mortal Programmers
Stephan February
@beardpappa
sfebruary@pivotal.io
http://hashbangbin.sh

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What is Category Theory
• Abstraction
• Objects
• Arrows (morphisms)

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Relation to Programming
f : A => B
g : B => C
g o f ~ g( f(A)) : A => C
domain(f)
codomain(f)

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Relation to Programming
What makes something a Category ?
composition :
f: A => B and g : B => Cgiven
g o f : A => C∃
objects :
morphisms : f, g
A, B, C
identity : id1: A => A or id2 : B => B
id1
id2

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Category Laws
id1
id2
Associative Law
Identity Law
(h o g) o f = h o (g o f)
f o id1 = id1 o f = f

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Functors
Categories : Functional Design Patterns
Apply a function f: x: Int => x2 to the sequence [1,2,3,4,5]
[1,2,3,4,5].map{ x => x * x }

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Functor

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Functor Recap
(A => B) (T[A] => T[B])
General Shape
Our Category

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Monads (homework)
Categories : Functional Design Patterns
(A => T[B]) (T[A] => T[B])
flatMap
General Shape

11. References
Programming
Scala
2nd Edition
StackOverFlow: A Monad Is Just a Monoid in the Category of Endofunctors. Whats The Problem ?
YouTube: Category Theory Lulz - Ken Scambler
YouTube: Category Theory, The Beginner's Introduction
Blog: Functors, Monads, Applicatives can be so simple
An Introduction to
Category Theory