Coinductive invertibility in higher categories (qtcat2026)

Invertibility is a crucial notion in category theory, providing the correct notion of sameness for objects within a category and equivalences of categories. This notion readily generalises to finite-dimensional higher categories inductively by replacing equalities with higher dimensional isomorphisms. The situation becomes more subtle with infinite-dimensional categories where there are different notions of invertibility. In this talk, we will give an introduction to weak ω-categories and we will study coinductively invertible cells within them. We will then describe computads with invertible generators as data for freely generating ω-categories. Licensed to the public under https://creativecommons.org/licenses/by/4.0/ about this event: https://pretalx.c3voc.de/qtcat-2026/talk/LARUFT/