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Having been in both worlds, I politely disagree. Almost all programmers have no use for category theory. Or even algebraic structures. It simply doesn't help with the problems programmers face. Categories are a tool for mathematicians, by mathematicians.
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I would frame the question differently, since I don't think the answer is monads (sorry Haskellers!). Why is it helpful for programmers to know about algebraic structures? Because structures are useful for modeling the world, and programs implicitly contain models of the world. twitter.com/wtgowers/statu…
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I'd love to hear about a time you solved a problem using a semilattice. How was that particular abstraction useful in a way that it was difficult without it?
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