Multicategory

Last updated Oct 7, 2024

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.

See also

• multicategory - symmetric multicategory, multicategories with a symmetry on their inputs.
• multicategory - premulticategory, multicategories without the interchange law.
• multicategory - malleable multicategory, multicategories with invertible composition, unbiased promonoidals.
• multicategory - promonoidal category, biased malleable multicategories.
• multicategory - promonoidals induce coherent multicategories

Related.

• polycategory, many-to-many linear version of a multicategory.
• monoidal category, representable version of a multicategory.

References

• Representable Multicategories (Hermida)
• Deductive Systems and Categories II: Standard Constructions and Closed Categories (Lambek)
• A Unified Framework for Generalized Multicategories (Cruttwell, Shulman, 2010)