Hom ω-categories of a computad are free

We provide a new description of the hom functor on weak ω-categories, and we show that it admits a left adjoint that we call the suspension functor. We then show that the hom functor preserves the property of being free on a computad, in contrast to the hom functor for strict ω-categories. Using the same technique, we define the opposite of an ω-category with respect to a set of dimensions, and we show that this construction also preserves the property of being free on a computad. Finally, we show that the constructions of opposites and homs commute.