Friday, July 11, 2014

A Category Theory Program for Concrete Thinkers

Finally some Haskellish content!

Anyway, it's taken me a few times of tilting at the Category Theory windmill to finally start to grasp it. One of my friends requested that I let him in on what finally worked for me, so this is for him. These videos by Steve Awodey were what really broke the logjam for me. Steve is good lecturer, and his presentation of the material works from the ground up. The best thing about those videos is that he gives examples of all of the concepts and explains what they are good for. I wish there were more of them; they don't cover a lot of ground.

There was one point where he started to lose me, though -- I failed to grasp his introduction of representable functors and the Yoneda Lemma. That is where some of The Catsters' videos came in handy. There's a useful guide to them on Brent Yorgey's blog. Others have raved about those videos, but I've always found them hard to get traction on, and felt that they lacked examples that would let me really connect to the subject. They really work for me as a second source, though. I am guessing that those who find them a good introduction probably need fewer concrete examples than I do.

That said, after watching two or three of the Awodey videos, The Catsters' videos started to make a lot more sense, and they were quite useful. They both filled in what I felt was the missing material on representables and Yoneda, and they cover more material than he did. I did find that after delving too deep into them, I again started to feel a lack of grounding. So I would appreciate any pointers that others might have to a more grounded introduction to some of the intermediate and advanced topics. Barring that, I think my next step will be Awodey's book.

Even with just the four Awodey videos and the first half or third of The Catsters' material, I've found that I can understand a lot of the functional programming discussion that was eluding me before. In fact, some of the blog posts from Bartosz Milewski and Gabriel Gonzalez have given me a more concrete grasp of some of the concepts.

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