Multicategories form a monoidal bicategory with multifunctors and multinatural transformations. Pseudomonoids in this monoidal bicategory are monoidal multicategories. Duoidales are duomulticategories. Any multicategory has an underlying category of 1-to-1 transformations. Any multicategory freely generates a category, called its contour.
- Representable Multicategories (Hermida)
- Deductive Systems and Categories II: Standard Constructions and Closed Categories (Lambek)
- A Unified Framework for Generalized Multicategories (Cruttwell, Shulman, 2010)