Re: [Haskell-beginners] Haskell and Category Theory

I can't help the OP unfortunately, but I find this topic to be pretty interesting. I'd be interested in exploring the mathematical foundations of CT. So, looking at this from a different aspect, what mathematics book / knowledge would I need in order to make Mac Lane's "Categories for the Working Mathematician" reasonably accessible, assuming UK A-Level further mathematics level or equivalent has been attained? Si On Mon, Feb 11, 2013 at 2:47 PM, Joe Fredette wrote:

While we await a reply, I will say that I found Benjamin Pierce's "Basic Category Theory for Computer Scientists" pretty readable, but will also readily admit my understanding of CT is not particularly deep or great. There are also some videos on youtube, particularly by [error792](1) which are worth watching, though they approach from a more math-oriented perspective (the video-author is a Mathematics Grad Student).

One thing that helped me a lot was learning a bit about Combinatorial Species -- I come from a math background, so having something firmly abstract to grab onto wrt examples of CT in use was (and is) useful, Brent has a [nice suite of posts](2) on the matter, and I'm sure will have some book/paper recommendations, I linked to just one of the posts on his blog, I'm sure you can navigate to the others.

The trick, I think, to learning CT is to realize it's a lot like Set theory -- there's a lot of abstract nonsense and definition shuffling (which error792's videos, iirc, note as "Soft Theorems"), and very little (immediate) connection to reality/more concrete tools. However, CT provides a framework of understanding which acts kind of like a highway-of-abstraction. When I can say, "A combinatorial species _is_ an endofunctor on the category of Sets and their Bijections", I necessarily know that if I can translate that category into another thing, then I can use my knowledge of species to inform my knowledge of that thing.

I'm probably telling this story wrong in some way, perhaps (if we don't mind a bit of thread hijacking) someone can improve my understanding of CT by correcting my likely and inevitable mistakes.

/Joe

(1) http://www.youtube.com/user/error792

(2) http://byorgey.wordpress.com/2012/11/20/combinatorial-species-definition/

On Mon, Feb 11, 2013 at 10:37 AM, Brent Yorgey wrote:

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On Sun, Feb 10, 2013 at 12:44:11PM -0500, Patrick Lynch wrote:

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Good morning, I've tried to read 5 books on Category Theory and finally have admitted defeat. What I'm looking for is simply a book that is geared to Haskell and Category that can be understood by mere mortals. I was trained as an Electrical Engineer, so my math is quite good, but I just don't get Category Theory from these books. If anyone can recomment a book on Category Theory and Haskell, written by a Computer Scientest [no more Mathematicians for me], I welcome it. Thanks, Patrick

Can you tell us which books you've tried to read?

-Brent

Well Brent is not going to say it I guess so someone needs to: Typeclassopedia http://www.haskell.org/haskellwiki/Typeclassopedia is required reading _______________________________________________ Beginners mailing list Beginners@haskell.org http://www.haskell.org/mailman/listinfo/beginners

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