it set objects are parenthesized permutations of , that is non-associative, non-commutative monomials on this set in which every letter appears exactly once.
morphisms between two objects are braids connecting each letter in to the same letter in . In other words, let be the canonical projection from the braid group to the symmetric group whose kernel is the pure braid group. Then, forgetting the parenthesization and viewing as permutations:
Then is an (ordinary) operad, the operadic structure being the same as for the non-colored version.