Hom ω$\omega$‐categories of a computad are free

Abstract We provide a new description of the hom functor on weak ‐categories, and 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 ‐categories. Using the same technique, we define the opposite of an ‐category with respect to a set of dimensions, and 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.