harmonic analysis?

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Dec 15, 2011 at 16:37	comment	added	Noah Snyder		For a simpler example of a "main theorem in category theory" there's the Yoneda lemma.
Dec 15, 2011 at 7:38	comment	added	Nicola Ciccoli		To add just a little bit to this answer I would say that the whole issue of Morita equivalence in C*-algebras (and, if you wish, in its geometrical counterpart i.e. Poisson geometry) certainly springs out from categorical ideas.
Dec 14, 2011 at 16:53	comment	added	Paul Siegel		Well, I decided to post that question after all: mathoverflow.net/questions/83437/…. I'm very curious now, and I hope you'll contribute!
Dec 14, 2011 at 16:01	comment	added	Paul Siegel		Thanks for the examples - based on this question I was actually contemplating posting a question of the form "What are the main theorems in category theory?" I confess that I don't know the statements of any of those results, and I have heard of only two of them. Thus I can make no intelligent statement about whether or not they have applications to analysis, except that it wouldn't surprise me if they come up in noncommutative geometry (given the flavor of some papers in that area).
Dec 14, 2011 at 13:04	comment	added	Martin Brandenburg		Concerning the first paragraph: There are some theorems in "pure" category theory which are nontrivial (General Adjoint Functor Theorem and the related Freyd's Representability Criterion, Beck's Monadicity Theorem, Recoqnition Theorems of locally presentable categories, Brown's Representability Theorem for triangulated categories,...). Unfortunately many people outside of category theory still believe that these general theorems are not useful at all, although the last decades have brought so many applications ...
Dec 13, 2011 at 22:27	history	answered	Paul Siegel	CC BY-SA 3.0