On associative n-categories and their formalization in proof assistants (cf.: Globular, homotopy.io):
David Reutter, Jamie Vicary, High-level methods for homotopy construction in associative $n$-categories, LICS ‘19: Proceedings of the 34th Annual ACM/IEEE Symposium on Logic in Computer ScienceJune 62 (2019) 1–13 [arXiv:1902.03831, doi:10.1109/LICS52264.2021.9470575]
Lukas Heidemann, David Reutter, Jamie Vicary, Zigzag normalisation for associative $n$-categories, Proceedings of the Thirty-Seventh Annual ACM/IEEE Symposium on Logic in Computer Science (LICS 2022) [arXiv:2205.08952, doi:10.1145/3531130.3533352]
Introducing a notion of fusion 2-categories:
On weak $\omega$-categories via computads construed as inductive types:
On G-crossed braided fusion categories via 3-categories:
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