Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On fibrations of Lie groupoids   As groupoids generalize groups, motivated by group extensions we consider a
kind of fibrations of Lie groupoids, called locally topological product Lie
groupoid fibrations with fiber $\sf A$, i.e., \[ 1\rightarrow {\sf A}
\rightarrow {\sf G} \rightarrow {\sf K}\rightarrow 1 \] where $\sf A,\sf G$ and
$\sf K$ are Lie groupoids. Similar to the theory of group extensions, we show
that the existence of locally topological product Lie groupoid fibrations with
fiber $\sf A$ over $\sf K$ is obstructed by a groupoid cohomology of $H^3_{\bar
\Lambda}({\sf K},Z_{\sf A})$, and these locally topological product Lie
groupoid fibrations are classified by $H^2_{\bar \Lambda}({\sf K},Z_{\sf A})$
once exists. Here $Z_{\sf A}$ is the center of $\sf A$. This generalizes the
theory of group extensions, of gerbes over manifolds/groupoids and etc.

16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph