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It is shown that if V is a local monoidal pseudovariety of semigroups, then K(m)V, D(m)V and LI(m)V are local. Other operators of the form Z(m)(_) are considered. In the process, results about the interplay between operators Z(m)(_) and (_)*D_k are obtained.doi:10.1142/s0218196713500112 fatcat:6jvwzr4rmbewpa2w4tai7k2gty