Simplicial sheaves of modules and Morita invariance of groupoid cohomology

Abstract

In this article we develop a unified framework for proving Morita invariance of cohomology theories associated to Lie groupoids. Our approach is to view these cohomology theories as arising from sheaves of modules on the nerve of the groupoid. We establish criteria for when such sheaves of modules give rise to Morita invariant cohomology theories.

41 page