2-nerves for bicategories

Details 2-nerves for bicategories 2-nerves for bicategories

2006-07-11

arxiv.org/abs/math/0607271v1

K-theory, 38(2):153-175, 2008

Mathematics

Category Theory

23 pages

Scientific paper

10.1007/s10977-007-9013-2

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.

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