  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.
