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I am just curious whether there are any (hard) theorems in mathematics, in a branch other than category theory, such that the proof requires the use of results in category theory in the sense that there is no obvious way to evade the abstract nonsense inside the proof using the theory inside the discipline ? Of course, the notions from category theory is used all the time and there is no way of avoiding it. This question emphasizes the use of results in category theory.

温泽海
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  • The construction of the Stone-Cech compactification is essentially just the proof of the special adjoint functor theorem. – subrosar Aug 26 '24 at 01:04
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    See also https://math.stackexchange.com/questions/1208375/honest-application-of-category-theory , its answers, and some of the answers to https://math.stackexchange.com/questions/2963724/easy-to-understand-examples-of-category-theoretic-theorems-that-are-useful . A common theme among the not-quite-answers to this question is that a simple Categorical fact makes a particular construction "the obvious thing to do here". – Eric Towers Aug 26 '24 at 02:05
  • I would say the linked questions show that this is a duplicate. – Martin Brandenburg Aug 26 '24 at 18:51

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