
TL;DR
This paper studies descent data in cosimplicial crossed groupoids, providing a combinatorial framework that models gerbes in algebraic geometry, and shows that weak equivalences induce bijections on gauge classes.
Contribution
It introduces a combinatorial abstraction for gerbe descent data and proves a key invariance property under weak equivalences.
Findings
Weak equivalences induce bijections on gauge equivalence classes
Provides a combinatorial model for descent data of gerbes
Bridges algebraic geometry and combinatorial groupoid theory
Abstract
We consider descent data in cosimplicial crossed groupoids. This is a combinatorial abstraction of the descent data for gerbes in algebraic geometry. The main result is this: a weak equivalence between cosimplicial crossed groupoids induces a bijection on gauge equivalence classes of descent data.
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