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I am wondering if it is possible to use the adjoint functors in topos theory for statements in analysis.

Any examples would be warmly welcomed. Though I would prefer simpler, atomic, lemmas or theorems if possible.

Thanks for your time.

Edit 1: Examples do not have to be restricted to analysis, I just thought those might be nice.

Edit 2: At this point even a comment would be nice.

Edit 3: To clarify, what I am looking for are theorems stated or proved using the adjoint functors relating to predicate calculus.

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  • $\begingroup$ You might be interested in this question and the answers there: math.stackexchange.com/questions/298912 . $\endgroup$ – Godot Aug 5 '13 at 10:06
  • $\begingroup$ Please check my answer and the following discussion. Categorists were furious and I received many downvotes, but as Did pointed out similar opinions are common outside category theory circles. I will say this again: I doubt you will find many non-trivial applications of category theory outside of category theory. So dear categorists: please show me that I am wrong and give me those striking examples of usefullness of category theory. $\endgroup$ – Godot Aug 5 '13 at 10:17
  • $\begingroup$ P.S.: dear categorists, we all heard about algebraic geometry. Please provide fresh examples. P.S.2: applications of category theory inside of category theory do not count. $\endgroup$ – Godot Aug 5 '13 at 10:22
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    $\begingroup$ Some statements (in algebra, mostly), even some classical ones, can be rephrased in terms of adjointness of functors, but that's not really the kind of application you want, is it? I'm thinking of Galois connections for example. I think expressing well known theorems that way is pointless, unless you get something new from it. $\endgroup$ – Ben Aug 5 '13 at 11:10
  • $\begingroup$ you are right ben, i am looking for something else. I am aware of the galois connection but as you say, that adjucntion doesnt really give us anything new. $\endgroup$ – user25470 Aug 9 '13 at 17:26
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In this paper you will find some "applications" of category theory to functional analysis:

www.eweb.unex.es/eweb/extracta/Vol-25-2/25J2Castillo.pdf

You will find more in its bibliography.

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  • $\begingroup$ Thanks Godot, it looks like an interesting article and i will read it. It isn't exactly what i was looking for but i'll give the question to you if nothing turns up $\endgroup$ – user25470 Aug 9 '13 at 19:30

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