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Title: 2-nerves for bicategories
Related: K-theory, Vol. 38, No. 2, (2008), p.153-175
DOI: 10.1007/s10977-007-9013-2
Publisher: Netherlands : Springer
Date: 2008
FoR/RFCD Code(s): 010100 Pure Mathematics
Author/Creator: Lack, Stephen
Author/Creator: Paoli, Simona
Description: 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.
Description: 23 page(s)
Subject Keyword: 010100 Pure Mathematics
Subject Keyword: Bicategory
Subject Keyword: Nerve
Subject Keyword: Homotopy Coherent nerve
Subject Keyword: 2-nerve
Subject Keyword: Simplicial category
Resource Type: journal article
Organisation: Macquarie University. Dept. of Mathematics

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