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