  The Catalan simplicial set $\mathbb{C}$ is known to classify skew-monoidal
categories in the sense that a map from $\mathbb{C}$ to a suitably defined
nerve of $\mathrm{Cat}$ is precisely a skew-monoidal category \cite{Catalan1}.
We extend this result to the case of skew monoidales internal to any monoidal
bicategory $\mathcal{B}$. We then show that monoidal bicategories themselves
are classified by maps from $\mathbb{C}$ to a suitably defined nerve of
$\mathrm{Bicat}$ and extend this result to obtain a definition of skew-monoidal
bicategory that aligns with existing theory.
