The 2-nerve of a 2-group and Deligne's determinant functors

Elhoim Sumano

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.

Keywords: Reduced homotopy n-type, geometric nerve for monoidal categories, 2-group, determinant functor, simplicial model category

2020 MSC: 18N50; 55P15; 55U35; 55P05; 18G45; 18F25

Theory and Applications of Categories, Vol. 37, 2021, No. 8, pp 227-265.

Published 2021-02-24.

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