English

Invertible cells in $\omega$-categories

Category Theory 2024-06-19 v1 Logic in Computer Science

Abstract

We study coinductive invertibility of cells in weak ω\omega-categories. We use the inductive presentation of weak ω\omega-categories via an adjunction with the category of computads, and show that invertible cells are closed under all operations of ω\omega-categories. Moreover, we give a simple criterion for invertibility in computads, together with an algorithm computing the data witnessing the invertibility, including the inverse, and the cancellation data.

Keywords

Cite

@article{arxiv.2406.12127,
  title  = {Invertible cells in $\omega$-categories},
  author = {Thibaut Benjamin and Ioannis Markakis},
  journal= {arXiv preprint arXiv:2406.12127},
  year   = {2024}
}
R2 v1 2026-06-28T17:09:36.731Z