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A Full and faithful Nerve for 2-categories

M. Bullejos·E. Faro·V. Blanco
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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.

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M. Bullejos, E. Faro, V. Blanco. 2004-09-24. A Full and faithful Nerve for 2-categories. https://arxiv.org/abs/math/0406615

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