Descent data of cosimplicial 2-groupoids

Details Descent data of cosimplicial 2-groupoids Descent data of cosimplicial 2-groupoids

2011-12-13

arxiv.org/abs/1112.3072v3

Mathematics

Algebraic Geometry

Scientific paper

We interpret descent data of a cosimplicial 2-groupoid as a 2-groupoid which in turn is the homotopy limit of the cosimplicial simplicial set gotten after applying the (2-)nerve on each cosimplicial degree. As a corollary, we generalize a result of Yekutieli and prove: if G \to H is a weak equivalence of cosimplicial 2-groupoids, the map Desc(G) \to Desc(H) is a weak equivalence of 2-groupoids.

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