  This paper discusses the question of how to recognize whether an operad is
E_n (ie. equivalent to the little n-cubes operad). A construction is given
which produces many new examples of E_n operads. This construction is developed
in the context of an infinite family of right adjoint constructions for
operads. Some other related constructions of E_n operads, so-called generalized
tensor products, are also described.
