2004/06/30 by Manuel Bullejos, M. Bullejos, Bullejos, M. +5 · 1 citation
Mathematics · Medicine · #18D05 #55U10 #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Intracranial Aneurysms: Treatment and Complications #math.CT #msc:18D05 #msc:55U10
paper · pdf · doi:10.48550/arxiv.math/0406615
8 pages
openalex publication_date 2004/06/30 · arxiv created 2004/09/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The notion of geometric nerve of a 2-category (Street, \citerefstreet) 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.