Computads with invertible generators for weak {\omega}-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.