2-nerves of bicategories
Stephen Lack and Simona Paoli
We describe a Cat-valued nerve of bicategories
which associates to every bicategory a simplicial object
in Cat, called its 2-nerve. This becomes the object-part
of a 2-functor N:NHom-->[Deltaop,Cat], where
NHom is a 2-category whose objects are bicategories and
whose 1-cells are normal homomorphisms. The 2-functor N is fully
faithful and 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 the Tamsamani weak
2-categories.
Click here to download a pdf file
of the complete paper, or get it from the
arXiv at
math.CT/0607271 (these
links are from the mirror in Australia).
Steve Lack
Last modified: Mon May 1 09:15:37 EST 2006