Has category theory solved major math problems?

Question

I am new to category theory.

Just wondering if category theory has solved any major problems for other mathematics fields?
What are the major applications of category theory?
Has anyone solved an open problem using category theory?
Particularly, has category theory solved any problems in number theory?

See: What is category theory useful for?; Most striking applications of category theory? on MO. — Najib Idrissi, Aug 27 '14 at 14:23
Be patient: you're not going to get any answers just yet. But suddenly, you'll get two or three very long answers. — James47, Aug 27 '14 at 21:43
Category theory has solved to formulate and to solve major math problems. — Martin Brandenburg, Sep 03 '14 at 12:44
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. — Jim, Aug 24 '19 at 13:57

Andrius Kulikauskas · Answer 1 · 2020-04-25T10:47:27.460

Emily Riehl's wonderful book Category Theory in Context is a book-length answer to your question. You can skip straight to the epilogue at the very end.

But, in particular, I think that the proofs of the Weil conjectures were driven by the category theoretical structure that Grothendieck and his colleagues worked out. This included a proof of a version of the Riemann hypothesis that is relevant for number theory.

Has category theory solved major math problems?

1 Answers1