michael_nielsen

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?

The Yoneda lemma is the obvious answer I think

What's the brief explanation of why I should care?

It’s a precise way to say “anything is perfectly determined by its relationship to everything else”

Or: if you can state how everything relates to thing X, you’ve defined X

“cayleys theorem but for all of mathematics” is a hyperbolic way to say it but not by as much as it sounds like

Nice analogy. Of course, Cayley's theorem is obvious, and I'd say no more than moderately interesting (though useful). Not trying to diss CT here! Just holding up a high standard: if CT was the most interesting result in group theory, we wouldn't think group theory interesting

Yeah. I think a lot of people like to say that the Yoneda lemma is the stupidest interesting thing in CT or something like that. It’s one of those “either trivial or absurdly deep” things.