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The 2-nerve of a 2-group and Deligne's determinant functors
Theory and applications of categories, Tome 37 (2021), pp. 227-265 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

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We prove that the bisimplicial set obtained by applying the 2-nerve functor of Lack and Paoli to a 2-group seen as a bicategory with one object, is a fibrant object in the universal simplicial replacement of Dugger of the model category of reduced homotopy 2-types. As an application we deduce a well known theorem about (non-symmetric) determinant functors for Waldhausen categories or derivators.

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Classification : 18N50, 55P15, 55U35, 55P05, 18G45, 18F25
Keywords: Reduced homotopy n-type, geometric nerve for monoidal categories, 2-group, determinant functor, simplicial model category 
@article{TAC_2021_37_a7,
     author = {Elhoim Sumano},
     title = {The 2-nerve of a 2-group and  {Deligne's} determinant functors},
     journal = {Theory and applications of categories},
     pages = {227--265},
     year = {2021},
     volume = {37},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2021_37_a7/}
}
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Elhoim Sumano. The 2-nerve of a 2-group and  Deligne's determinant functors. Theory and applications of categories, Tome 37 (2021), pp. 227-265. http://geodesic.mathdoc.fr/item/TAC_2021_37_a7/