Combinatorial Descent Data for Gerbes

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.Comment: 13 pages, 2 figures. Final version, to appear in J. Noncommutative Geometr