I strongly agree!
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Replying to @Meaningness @AmbrosialArts and
But, getting the intuitions, and understanding mathematical topics from multiple perspectives, is not a matter of mathematical logic (as it is currently constituted anyway)
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Replying to @Meaningness @AmbrosialArts and
The whole point of category theory is to provide just this perspective. (Contemporary CT research goes off in all kinds of directions, but that's to be expected.) What's needed is very basic category theory, with an eye to addressing the basics maths of interest.
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Replying to @StephenPiment @AmbrosialArts and
Yes… I did category theory with G-C Rota, before anyone else in computer science had heard of it :) FWIW, I think it’s not the right thing, although it has the right aim.
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Replying to @Meaningness @StephenPiment and
This alternative framework developed by my then office mate David McAllester seems more nearly right to me: https://arxiv.org/abs/1407.7274
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It has a generalized understanding of isomorphism, which allows you to express things like “everything linear is really just matrix multiplication” rigorously
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