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.
Variants
- comulticategory
- symmetric multicategory, multicategories with a symmetry on their inputs.
- premulticategory, multicategories without the interchange law.
- malleable multicategory, multicategories with invertible composition, unbiased promonoidals.
- promonoidal category, biased malleable multicategories.
- Cartesian multicategory and cocartesian comulticategory.
- distributive multicategory
- polycategory, many-to-many linear version of a multicategory.
- monoidal category, representable version of a multicategory.
- duomulticategory
Related.
- algebra over a multicategory
- Being multicategorical in each variable is the Chu construction
- promonoidals induce coherent multicategories
- lax monoidal functor, representable version of a multifunctor.
- underlying category of a multicategory
References