Higher Descent Data as a Homotopy Limit

TL;DR

This paper introduces a homotopy-theoretic framework for understanding descent data in higher category theory, generalizing classical concepts to 2-groupoids and beyond, with potential applications in higher-dimensional algebra.

Contribution

It defines the 2-groupoid of descent data as a homotopy limit, extending the concept to n-groupoids for higher-dimensional descent analysis.

Findings

Homotopy limit representation of descent data for 2-groupoids

Extension of the framework to n-groupoids

Provides a new perspective on higher-dimensional descent data

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.