Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On two notions of a Gerbe over a stack   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 $F\colon \mathcal{D}\rightarrow \mathcal{C}$,
such that $F$ and the diagonal map $\Delta_F\colon \mathcal{D}\rightarrow
\mathcal{D}\times_{\mathcal{C}}\mathcal{D}$ are epimorphisms. This paper
explores the relationship between a gerbe defined above and a Morita
equivalence class of a Lie groupoid extension.

13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int