ACT
MIT 2020 - Programming with Categories Course

MIT 2020 - Programming with Categories Course

• By Brendan Fong, Bartosz Milewski and David Spivak

• Course page

• Course teaser (non-technical)

Lectures

These discussions on the Azimuth Forum each begin with the MIT lecture video and link to David Dalrymple’s class notes.

• Lecture 0 - Welcome to programming with categories - Brendan, David, Bartosz

• Lecture 1 - Sets, functions and categories - David

• Lecture 2 - Examples of categories; begin Haskell - Brendan

• Lecture 3 - Building up theory for Haskell - Bartosz

• Lecture 4 - Functors and natural transformations - David

• Lecture 5 - So, functors! - Bartosz

• Lecture 6 - Terminal and initial objects; products - Brendan

• Lecture 7 - Universal properties: products, coproducts and exponentials - David

• Lecture 8 - Natural transformations, currying and adjunctions - Bartosz and Brendan

• Lecture 9 - Recursion, algebras and F-algebras - Bartosz and Brendan

• Lecture 10 - Coalgebra - David

• Lecture 11 - Bartosz

• Lecture 12 - Monads - Brendan

• Lecture 13 - Examples of monads, Kleisli categories - David

• Lecture 14 - Monads from the perspective of a programmer - Bartosz

• Lecture 15 - Monoidal categories - David

• Lecture 16 - Kinds of functors - Brendan

• Lecture 17 - Protofunctors - Bartosz

Exercises

Discussions on the Azimuth Forum:

• Question 1.1 - Functions in mathematics and Haskell

• Question 1.2 - A tiny category

• Question 1.3 - Is it an isomorphism

• Question 1.4 - Almost categories

• Question 1.5 - Monoids

• Question 1.6 - Preorders

• Question 2.1 - Functors out of set

• Question 2.2 - Constant functors

• Question 2.3 - The naturality of the diagonal

• Question 2.4 - Uniqueness of universal objects

• Question 2.6 - Products in Hask

• Question 2.7 - The product of categories

• Question 2.8 - Bifunctors

• Question 2.9 - Programming with categories

• Question 3.2 - Catamorphisms

• Question 3.3 - Naturals

• Question 3.4 - Merge sort

• Question 3.5 - Monoids as list algebras

• Question 3.6 - Hello world

• Question 3.7 - The tree monad