We define inductively the opposites of a weak globular $\omega$\-category with respect to a set of dimensions, and we show that the properties of being free on a globular set or a computad are preserved under forming opposites. We then provide a new description of the hom functor on $\omega$\-categories, and we show that it admits a left adjoint that we construct explicitly and call the suspension functor. We also show that the hom functor preserves the property of being free on computad, and that the opposites of a hom $\omega$\-category are hom $\omega$\-categories of opposites of the original $\omega$\-category.

翻译：我们归纳定义了弱球状$ω$\-范畴关于一组维度的对偶，并证明了在形成对偶后，球状集或计算域上的自由性质得以保持。随后，我们给出了$ω$\-范畴上同态函子的新描述，并证明它存在一个左伴随，我们将其显式构造并称为悬浮函子。我们还证明了同态函子保持计算域上的自由性质，并且一个同态$ω$\-范畴的对偶正是原始$ω$\-范畴对偶的同态$ω$\-范畴。