Computads with invertible generators for weak ω-categories

We extend the notion of computads for weak $\omega$-categories to allow marking certain generators as invertible, and describe inductively the free $\omega$-categories they generate. This gives a simple, finite description of the walking equivalences, the $\omega$-categories classifying invertible cells. We then construct a coreflection from generalised to ordinary computads, preserving the generated $\omega$-categories, and conclude that $\omega$-categories generated by generalised computads are cofibrant. Finally, we study the subcategory of generalised computads and generator-preserving morphisms, and show that it is a presheaf topos, similarly to the case of ordinary computads.