Invertible cells in $\omega$-categories
<|reference_start|>Invertible cells in $\omega$-categories: We study coinductive invertibility of cells in weak $\omega$-categories. We use the inductive presentation of weak $\omega$-categories via an adjunction with the category of computads, and show that invertible cells are closed under all operations of $\omega$-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.<|reference_end|>
@article{benjamin2024invertible,
    title={Invertible cells in $\omega$-categories},
    author={Thibaut Benjamin and Ioannis Markakis},
    journal={arXiv preprint arXiv:2406.12127},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.12127},
    primaryClass={math.CT cs.LO}
}