Programming with Categories - Lecture 3

Lecturers: Brendan Fong, Bartosz Milewski, David Spivak

Summary: In this course we explain how category theory—a branch of mathematics known for its ability to organize the key abstractions that structure much of the mathematical universe—has become useful for writing elegant and maintainable code. In particular, we'll use examples from the Haskell programming language to motivate category-theoretic constructs, and then explain these constructs from a more abstract and inclusive viewpoint. Hands-on programming exercises will be used to demonstrate categorical ideas like "the universal property of products" in working Haskell code.

We will assume no background knowledge on behalf of the student, starting from scratch on both the programming and mathematics.

(Video: Paolo Perrone.)

[WayOfTheCode]

I love that Topos exists on YouTube. All I have learned about category theory is either through Bartosz's blog and channel, or from here

[zapazap]

So nice to be combining the abstract categorical stuff (which I like) with the programming stuff (which I can grok).

[kaushaltimilsina]

Bartosz's explanations are really enjoyable and really great for understanding! I learned so much from even just this one lecture and it was really enjoyable.

[owen]

Bartosz: and now for something completely different

[chaoshengzhe]

1.25x speed Bartosz sounds more natural. 🧐

[alexhamilton]

When will he release his 4th part on Category theory for programmers, the 3rd part didn't finish all the content of the last section in his book : (

[bblfish]

When Bartosz speaks of functions that never return being one reason for Hask not being a full category, I suppose that practically speaking in many cases a function that takes too long is equivalent to a function that never returns. Consider a search engine that needs to return a result in a fraction of a second. For that application a minute is close to eternity. I mention that as it illustrates how practical requirements have an impact on the theory.

[michaelkohlhaas]

Still talking about function composition after so many lectures? There is really no categorical meat in programming!

[michaelkohlhaas]

Funny why they don't use a computer for demonstration purposes! Ridiculous!