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That's just one subfield of mathematics. During my PhD, I barely touched adjoints and fixed points. Though, many fields of math so indeed have this sort of repe
by atq2119 4y ago
That's just one subfield of mathematics. During my PhD, I barely touched adjoints and fixed points. Though, many fields of math so indeed have this sort of repeating pattern. It's just not the same for all of them.
- adamnemecek 4y agoWhat subfield do you think I'm talking about? Which subfield doesn't involve adjoints and fixed points?
- bollu 4y agoMost "hard results" in any subfield of math cannot be derived from pure categorical nonsense like adjunctions. At some point, you have to roll up your sleeve and do the work. How would you prove the tychonoff theorem purely with adjunctions? How about the representation theorem of finitely presented abelian groups? And on and on and on...