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added two sentences to the Idea-section, to provide more of an explanation:
If the gauge group is SU(N) and fermions are in the fundamental representation of dimension , so that has a linear basis of elements, one says that these are colors of the given fermion particle.
Hence, more generally one could reasonably say that the “number of colors” of a given fundamental particle in gauge theory is physics synonym for the choice of linear representation of the gauge group that defines this particle.
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