nLab bimulticategory

Contents

Context

Monoidal categories

monoidal categories

With braiding

With duals for objects

With duals for morphisms

With traces

Closed structure

Special sorts of products

Semisimplicity

Morphisms

Internal monoids

Examples

Theorems

In higher category theory

Higher category theory

higher category theory

Basic concepts

Basic theorems

Applications

Models

Morphisms

Functors

Universal constructions

Extra properties and structure

1-categorical presentations

Category theory

Contents

Idea

Just as a multicategory generalises a monoidal category, a bimulticategory generalises a monoidal bicategory.

A 2-multicategory is a Cat-enriched multicategory, which is a strict bimulticategory.

(Note that the term multibicategory is used in the literature for a different concept: namely a virtual bicategory.)

References

Bimulticategories (and their pseudofunctors, transformations, and modifications) are introduced in Definition 4.2.29 of the following, where it is also proven that every monoidal bicategory induces a bimulticategory:

  • Philip Saville, Cartesian closed bicategories: type theory and coherence. PhD thesis, 2020. pdf.

A definition of representable bimulticategory is proposed therein, but the relationship with monoidal bicategories is not established.

Created on June 9, 2025 at 17:10:53. See the history of this page for a list of all contributions to it.