No, he translates the sum back to colors. E.g., there is a map f:colors->H with an inverse g:H->colors and he says the color g(sum(f(hat))) where the index ha

No, he translates the sum back to colors. E.g., there is a map f:colors->H with an inverse g:H->colors and he says the color g(sum(f(hat))) where the index hat ranges over all of the hats.