For this question I'm assuming a person who knows both basic set theory and category theory (functors, natural transformations, limits, colimits, adjacents).
There are theorem proofs that get "easier" (not rigorouly I mean something like shorter, easier to read, needing less tools) when you use category theory tools rather than set theory ones, some examples may be found in multilinear algebra.
I'd like a "the other way" theorem: easy proof using set theory, complicated proof using category theory. I want theorem with at least two known proofs, at least one using category theory tools and at least one using set theory ones.
Thank you very much for any idea!