Let $\mathcal{G}$ be a Lie groupoid. The category $B\mathcal{G}$ of principal $\mathcal{G}$-bundles defines a differentiable stack. On the other hand, given a differentiable stack $\mathcal{D}$, there exists a Lie groupoid $\mathcal{H}$ such that $B\mathcal{H}$ is isomorphic to $\mathcal{D}$. Define a gerbe over a stack as a morphism of stacks $F:\mathcal{D}\to \mathcal{C}$, such that F and the diagonal map ${\mathrm{\Delta }}_F:\mathcal{D}\to \mathcal{D}{\times }_{\mathcal{C}}\mathcal{D}$ are epimorphisms. This paper explores the relationship between a gerbe defined above and a Morita equivalence class of a Lie groupoid extension.

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关于栈上的gerbe的两个概念

让 $\mathcal{G}$成为李群怪。类别$乙\mathcal{G}$ 本金 $\mathcal{G}$-bundles定义可区分的堆栈。另一方面，给定一个可微的堆栈$\mathcal{d}$，存在一个李群 $\mathcal{H}$ 这样 $乙\mathcal{H}$ 同构 $\mathcal{d}$。将堆栈上的gerbe定义为堆栈的态射$F：\mathcal{d}\to \mathcal{C}$，如F和对角线图${\mathrm{\Delta }}_F：\mathcal{d}\to \mathcal{d}{\times }_{\mathcal{C}}\mathcal{d}$是种质。本文探讨了上面定义的gerbe和Lie groupoid扩展的Morita等价类之间的关系。