On two notions of a gerbe over a stack

Abstract

Let G be a Lie groupoid. The category BG of principal G-bundles defines a differentiable stack. On the other hand, given a differentiable stack D, there exists a Lie groupoid H such that BH is isomorphic to D. We define a gerbe over a stack as a morphism of stacks F : D -> C, such that F and the diagonal map Delta_F : D -> D times_C D are epimorphisms. In this talk we explore the relationship between a gerbe, as defined above, and a Morita equivalence class of a Lie groupoid extension. This talk is based on our paper (j/w Saikat Chatterjee) titled "On two notions of a gerbe over a stack" (https://doi.org/10.1016/j.bulsci.2020.102886).