  It was shown in a recent paper by Boavida de Brito and Weiss that a
well-known construction which to a plain (=monochromatic) topological operad
associates a topological category and a functor from it to the category of
finite sets is homotopically fully faithful, under mild conditions on the
operads. The main result here is a generalization of that statement to
k-truncated plain topological operads. A k-truncated operad is a weaker version
of operad where all operations have arity at most k.
