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I had a few suggestions until I saw your last sentence. There is no particular category theoretic structure in GUTs apart from what category structure there is in general QFT and gauge theory.
Here are two suggestions I had before I saw your last sentence:
on the need for monoidal categories: John Baez, Quantum Quandaries: a Category-Theoretic Perspective
on the need for sheaves and stacks: Ragnar Eggertsson, Stacks in Gauge theory
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