A Full and Faithful Nerve For
نویسندگان
چکیده
The notion of geometric nerve of a 2-category (Street, [18]) 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 sim-plicial 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.
منابع مشابه
A Full and Faithful Nerve for 2-Categories
We prove that there is a full and faithful nerve functor defined on the category 2-Cat lax of 2-categories and (normal) lax 2-functors. This functor extends the usual notion of nerve of a category and it coincides on objects with the so-called geometric nerve of a 2-category or of a 2-groupoid. We also show that (normal) lax 2-natural transformations produce homotopies of a special kind, and th...
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تاریخ انتشار 2005