A Full and faithful Nerve for 2-categories
Category Theory
2007-05-23 v2
Abstract
The notion of geometric nerve of a 2-category (Street, \cite{refstreet}) 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.
Cite
@article{arxiv.math/0406615,
title = {A Full and faithful Nerve for 2-categories},
author = {M. Bullejos and E. Faro and V. Blanco},
journal= {arXiv preprint arXiv:math/0406615},
year = {2007}
}
Comments
8 pages