3 problems

A 3-crossed module is a structure consisting of four groups and six kinds of liftings, as formulated in this paper. Let $\mathcal{C}$ be the category of these 3-crossed modules. Hi…

Campion's conjecture. The cubes might provide a dense presentation for $(\infty,\omega)$-categories.

Let $Q$ be the full dense monoidal subcategory of ${\omega\textnormal{-Cat}}$ whose objects are the free $\omega$-categories $O(I^n)$ on parity $n$-cubes, with tensor product…