  We construct generalized multicategories associated to an arbitrary operad in
Cat that is $\Sigma$-free. The construction generalizes the passage to
symmetric multicategories from permutative categories, which is the case when
the operad is the categorical version of the Barratt-Eccles operad. The main
theorem is that there is an adjoint pair relating algebras over the operad to
this sort of generalized multicategory. The construction is flexible enough to
allow for equivariant generalizations.
