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Physics involves the crown jewels of modern mathematics, so something deep might be going on, but, second, these insights remain piecemeal. There is a field of mathematics here, another there. One could get the idea that somehow all this wants to be put together into one coherent formal story, only that maybe the kind of maths used these days is not quite sufficient for doing so.
Category theory is an approach to understand these connections and categorise them. In this sense, category theory is a meta-theory of mathematics.
See also: Categorifying Fundamental Physics by John Baez