A full and faithful nerve for 2-categories

被引：10
|
作者：
Bullejos, M [1 ]
Faro, E
Blanco, V
机构：
[1] Univ Granada, Dept Algebra, E-18071 Granada, Spain
[2] Univ Vigo, Dept Appl Math, Vigo 36207, Spain
来源：
APPLIED CATEGORICAL STRUCTURES | 2005年 / 13卷 / 03期
关键词：
Mathematical Logic; Discrete Geometry; Representation Theorem; Homotopy Class; Faithful Functor;
D O I：
10.1007/s10485-005-2957-6
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The notion of geometric nerve of a 2-category (Street, J. Pure Appl. Algebra 49 (1987), 283-335) provides a full and faithful functor if regarded as defined on the category of 2-categories and lax 2-functors. Furthermore, lax 2-natural transformations between lax 2-functors give rise to homotopies between the corresponding simplicial maps. These facts allow us to prove a representation theorem of the general non-abelian cohomology of groupoids (classifying non-abelian extensions of groupoids) by means of homotopy classes of simplicial maps.
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页码：223 / 233
页数：11
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