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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 $\mathbf{N}$ of dimension $N$, so that $\mathbf{N}$ has a linear basis of $N$ elements, one says that these are $N$ 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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