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Why category theory is needed?

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To describe anyon statistics, it is said that the modular tensor category is suitable for this aim, in particular for describing fusion rule.

However, the fusion rule seems to be just a decomposition of representation of the braid group into the sum of irreducible representations. I suppose that group theory and its representation theory are enough to discuss such a decomposition. My question is why the modular tensor category is more suitable than group theory.

asked Jul 19, 2020 in Theoretical Physics by K_Phys (30 points) [ no revision ]

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