  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.
