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All:

I am new to category theory.

Just wonder if category theory has solved any major math problems for other mathematics fields? or what are the major applications of the category theory ?

Particularly, has category theory solved any problems in number theory ?

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  • 6
    $\begingroup$ See: What is category theory useful for?; Most striking applications of category theory? on MO. $\endgroup$ – Najib Idrissi Aug 27 '14 at 14:23
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    $\begingroup$ Be patient: you're not going to get any answers just yet. But suddenly, you'll get two or three very long answers. $\endgroup$ – James47 Aug 27 '14 at 21:43
  • $\begingroup$ Category theory has solved to formulate and to solve major math problems. $\endgroup$ – Martin Brandenburg Sep 3 '14 at 12:44
  • $\begingroup$ Solely by itself there are probably a few examples, but that's maybe the wrong way to look at it. Category theory is the language in which most modern algebraic mathematics is phrased in and understood with respect to. It's not that category theory solves the problems, it's that category theory lets us say what the problems are. $\endgroup$ – Jim 10 hours ago

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