The Catalan simplicial set ℂ is known to classify skew-monoidal categories in the sense that a map from ℂ to a suitably defined nerve of Cat is precisely a skew-monoidal category (Buckley et al. 2014). We extend this result to the case of skew monoidales internal to any monoidal bicategory B. We then show that monoidal bicategories themselves are classified by maps from ℂ to a suitably defined nerve of Bicat and extend this result to obtain a definition of skew-monoidal bicategory that aligns with existing theory.
- Simplicial set
- Skew monoidal