The periodic table of $n$-categories for low dimensions II: degenerate tricategories

Understand

We continue the project begun in ``The periodic table of $n$-categories for low dimensions I'' by examining degenerate tricategories and comparing them with the structures predicted by the Periodic table.

• For triply degenerate tricategories we exhibit a triequivalence with the partially discrete tricategory of commutative monoids.
• For the doubly degenerate case we explain how to construct a braided monoidal category from a given doubly degenerate category, but show that this does not induce a straightforward comparison between \bfseries{BrMonCat} and \bfseries{Tricat}.
• We show how to alter the natural structure of \bfseries{Tricat} in two different ways to provide a comparison, but show that only the more brutal alteration yields an equivalence.