What insights does category theory offer in terms of grand unified theories? Any references to books or papers that give categorical descriptions of any of the common grand unified theories would be helpful.
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2Related: http://physics.stackexchange.com/q/3759/2451 and links therein. – Qmechanic Apr 22 '15 at 15:33
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If you are not only concerned with the "common" approaches to grand unified theories, there is something called the "topos approach" to quantum theory (see e.g. http://arxiv.org/pdf/1207.1744v1.pdf for a thorough introduction). They try to derive quantum theory in a category-related language of topoi, hoping to thereby get rid of observers, which they see as the crucial step towards uniting the theory with general relativity. – Martin Apr 24 '15 at 14:04