Computads with invertible generators for weak ω-categories

Thibaut Benjamin; Camil Champin; Ioannis Markakis

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arXiv · 2606.30254

Computads with invertible generators for weak ω-categories

Thibaut Benjamin·Camil Champin·Ioannis Markakis

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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.

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BibTeX RIS

Thibaut Benjamin, Camil Champin, Ioannis Markakis. 2026-06-29. Computads with invertible generators for weak ω-categories. https://arxiv.org/abs/2606.30254

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