I want to clarify, I am not trivializing the work of category theorist. It is a field of mathematics which provides a useful framework for algebraic geometers and algebraic topologists, and has even been fruitfully applied outside of math.

A personal favorite of CT generalizing an existing idea is in knot theory the khovanov homology detects the unknot, which is an amazing feat for a knot invariant. Bar Natan covers the construction well: https://arxiv.org/abs/math/0201043

However for some reason this particular field of math is a lightning rod for quacks. I don't really know why, but that is the way things are now.