Category Theory: the Video Lectures

I just wrapped up watching Bartosz Milewski’s YouTube series on category theory. If you are at all interested in functional programming, this is an outstanding set of lectures.

The course covers category theory, a rather abstract branch of mathematics. Throughout the twenty videos, Milewski takes us through the landscape of category theory, grounding it as much as possible in the language and concepts of programming. Some of Milewski’s examples are in Haskell but you don’t need to know that language to understand what’s going on. Similarly, other examples are in C++, but it’s clear from the context what he means even if you’ve never seen a line of the language.

I came into this course with a fair knowledge of functional programming and a less-than-fair knowledge of category theory. Watching these videos has given me a much better understanding of the topic and has really cleared up some of the trickier concepts in functional programming like monads.

For further reading, Milewski has a blog full of posts on the topic and a group has (with permission) turned his posts into a book. There are also two more courses on category theory that Milewski has put together, helping us dig even further into the topic.

If you are interested in the series, don’t get too distracted by the intentionally-opaque examples. I’ve seen this in undergraduate courses I took on logic, where the professor wants to ensure that you don’t get stuck thinking about a specific example when explaining a general concept, as though the specific example were the only case. Milewski does a good job of combining the highly-general drawings of categories and how elements in categories can map to other categories via functors but then brings it down to examples we’re more familiar using, particularly with sets. There’s a balancing act involved in these examples and I think Milewski has that act pretty well covered.

It may take you a month or three to get through all of these videos, but I definitely recommend them. From here, I’m going to work through the book and fill in more gaps.

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