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A Full and faithful Nerve for 2-categories

M. Bullejos, E. Faro, V. Blanco

math.CTarXiv:math/0406615

Abstract

The notion of geometric nerve of a 2-category (Street, 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.

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