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 -