Trying Category Theory again. Does anyone have good intros for someone who:
* Has strong background in CS, PL/types and *operational* semantics, but none in denotational
* Knows what a group is, but no topology or real analysis
* Does NOT learn from pictures
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I have Pierce's Category Theory for Computer Scientists book on loan from a friend that is short but nifty - it has some examples relating it to little functional languages. But I'm still a beginner at this stuff, so take my recommendation with a grain of salt.
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It’s well written, but I remember concluding that it doesn’t actually teach category theory...
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I've not yet really applied myself to learning this stuff (juggling lots of things), but I wouldn't be surprised if I agreed with you after reading it more closely.
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Big challenge I face is lots of the category theory stuff is geared towards mathematicians, and it was nice to have some programming language examples in there. Maybe combined with something else it could be useful?
From memory the signatures of things like categories and functors etc. were laid in a way that I could imagine transferring it to a programming language. Where as the more 'mathematical' texts had the signatures of stuff smushed into prose. But my memory could be playing tricks.
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Sure, I'm happy to rant about math writing, I'm just taking a day off from that.
I liked a lot better Peter Smith's suggestions — his notes and then Leinster's book. I don't like Awodey's, but IIRC my problem there were with later chapters.
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What are some good programming language examples? I have the feeling that most are like “any model of STλC is a CCC”, which is not really an example (though motivating). Meanwhile, models are often random mathematical structures, so ultimately these examples can't be avoided.
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Ah, that's a good point - I'm very much out of my depth with this stuff, but the example of a little functional language Peirce's book was helpful, and then helped me then go to getting my head around the other mathematical examples.
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