TY - JOUR

T1 - 2-nerves for bicategories

AU - Lack, Stephen

AU - Paoli, Simona

PY - 2008/1

Y1 - 2008/1

N2 - We describe a Cat-valued nerve of bicategories, which associates to every bicategory a simplicial object in Cat, called the 2-nerve. This becomes the object part of a 2-functor N : NHom → [Δop,Cat], where NHom is a 2-category whose objects are bicategories and whose 1-cells are normal homomorphisms of bicategories. 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 Tamsamani weak 2-categories.

AB - We describe a Cat-valued nerve of bicategories, which associates to every bicategory a simplicial object in Cat, called the 2-nerve. This becomes the object part of a 2-functor N : NHom → [Δop,Cat], where NHom is a 2-category whose objects are bicategories and whose 1-cells are normal homomorphisms of bicategories. 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 Tamsamani weak 2-categories.

UR - http://www.scopus.com/inward/record.url?scp=38349014645&partnerID=8YFLogxK

U2 - 10.1007/s10977-007-9013-2

DO - 10.1007/s10977-007-9013-2

M3 - Article

AN - SCOPUS:38349014645

SN - 0920-3036

VL - 38

SP - 153

EP - 175

JO - K-Theory: interdisciplinary journal for the development, application and influence of K-theory in the mathematical sciences

JF - K-Theory: interdisciplinary journal for the development, application and influence of K-theory in the mathematical sciences

IS - 2

ER -