Most scientific & mathematical disciplines I know of have results that educated outsiders can appreciate and go "wow" after a brief acquaintance, even without understanding the details. Does anyone know of such a result for category theory?
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Replying to @michael_nielsen
(Not in amswer to your question, per se). I think my favorite, if somewhat unsatisfying, answer to “why category theory” is that “it makes trivial results in math trivially trivial”.
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Replying to @3blue1brown @michael_nielsen
Hmmm I also don't have a "wow" application, but before category theory, you had a bunch of different competing notions in (co-)homology, e.g., singular (i.e. "continuous"), simplicial (i.e. combinatorial), de Rham (geometric), Cech, etc, each doing a completely different (cont'd)
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2/ calculation but getting basically the same answer. Category theory, as introduced by Eilenberg/Mac Lane, was meant to explain "why". The definitions were all different, the objects were all different, but their relationships to each other were "functorial". So if a (cont'd)
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3/3 combinatorial calculation became impossible, just switch to a topological one. Or geometrize, etc., and you'd be guaranteed to get the right answer to your original question. Hope this helps? The idea became so useful it took off like wildfire, see: https://en.wikipedia.org/wiki/Timeline_of_category_theory_and_related_mathematics …
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This is very interesting, thanks.
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