2-nerves for bicategories
2-nerves for bicategories
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2-二类神经
DOI：
10.1007/s10977-007-9013-2
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发表时间：
2006
期刊：
影响因子：
--
通讯作者：
Simona Paoli
中科院分区：
文献类型：
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作者：
Stephen Lack;Simona Paoli
我们描述了一个猫值神经的bicategories，其中关联到每一个bicategory一个单纯的对象在猫，称为2神经。我们定义了一个2类NHom的对象是bicategories和其1细胞是正常的同态的bicategories，在这样一种方式，2-神经建设成为一个完整的嵌入NHom的2类的单纯对象在猫。这个嵌入有一个左双伴随，我们描述其图像。双范畴的2-神经总是Tamsamani意义下的弱2-范畴，并且证明了NHom与对象为Tamsamani弱2-范畴的某个2-范畴是双等价的.
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.