2-nerves for bicategories
By Stephen Lack, Simona Paoli. 2006
67 citations recorded by the source corpus.
We describe a Cat-valued nerve of bicategories, which associates to every bicategory a simplicial object in Cat, called the 2-nerve. We define a 2-category NHom whose objects are bicategories and whose 1-cells are normal homomorphisms of bicategories, in such a way that the 2-nerve construction becomes a full embedding of NHom in the 2-category of simplicial objects in Cat. This embedding has a left biadjoint, and we characterize its image. The 2-nerve of a bicategory is always a weak 2-category in the sense of Tamsamani, and we show that NHom is biequivalent to a certain 2-category whose objects are Tamsamani weak 2-categories.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/e31a5413a17ab92039269c472944b75b5ebab56c
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Algebra and Number Theory
- Michael Shulman
- Richard Garner
- Stephen Lack
- Emily Riehl
- Nicola Gambino
- R. Haugseng
- Ieke Moerdijk
- C. Berger
In Geometry and Topology
- Michael Shulman
- Richard Garner
- Stephen Lack
- Emily Riehl
- Dominic R. Verity
- Aaron D. Lauda
- Nicola Gambino
- Mark Weber
In Mathematical Physics
- Michael Shulman
- Richard Garner
- Stephen Lack
- Emily Riehl
- Dominic R. Verity
- Aaron D. Lauda
- Nicola Gambino
- Mark Weber
Citations in the corpus
- A 2-Categories Companion (2007, background): “This section is particularly light on details; see [38] for more.”
- Enriched categories as a free cocompletion (2013, methodology): “V-icons Following [22,21], a V-icon is essentially an oplax V-transformation whose 1-cell components γx are identities; as in the unenriched case, we can formulate an equivalent notion more simply.”