Higher Descent Data as a Homotopy Limit

2011/12/13 by Matan Prasma, Prasma, Matan
Mathematics · #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG

paper · pdf · doi:10.48550/arxiv.1112.3072

Appeared in JHRS

openalex publication_date 2011/12/13 · arxiv created 2015/07/15 · arxiv updated 2015/07/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define the 2-groupoid of descent data assigned to a cosimplicial 2-groupoid and present it as the homotopy limit of the cosimplicial space gotten after applying the 2-nerve in each cosimplicial degree. This can be applied also to the case of n-groupoids thus providing an analogous presentation of "descent data" in higher dimensions.

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