Internal bicategories

Abstract

We define bicategories internal to 2-categories. When the ambient 2-category is symmetric monoidal categories, this provides a convenient framework for encoding the structures of a symmetric monoidal 3-category. This framework is well suited to examples arising in geometry and algebra, such as the 3-category of bordisms or the 3-category of conformal nets.

Added references, removed appendices

References in corpus (4)

• Monoidal 2-structure of Bimodule Categories
• Constructing symmetric monoidal bicategories
• Conformal nets and local field theory
• Conformal nets III: fusion of defects

Cited by in corpus (5)

• A 3-categorical perspective on G-crossed braided categories
• Coherence for Frobenius pseudomonoids and the geometry of linear proofs
• Conformal nets III: fusion of defects
• Alternative notion to intercategories: part I. A tricategory of double categories
• Lifting bicategories through the Grothendieck construction