Computads with invertible generators for weak ω-categories

Abstract

We extend the notion of computads for weak \(ω\)-categories to allow marking certain generators as invertible, and describe inductively the free \(ω\)-categories they generate. This gives a simple, finite description of the walking equivalences, the \(ω\)-categories classifying invertible cells. We then construct a coreflection from generalised to ordinary computads, preserving the generated \(ω\)-categories, and conclude that \(ω\)-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.