Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extensions of $\infty$-group sheaves   Let $\mathscr X$ be an $\infty$-topos, for example the $\infty$-category of
simplicial sheaves on a Grothendieck site. Then $\infty$-group sheaves are
group objects in $\mathscr X$. Let $A\in\mathrm{Grp}\mathscr X$ be such a group
object. Then as $\mathscr X$ is an $\infty$-topos, there exists a universal
$\mathbf BA$-fiber bundle $\mathbf BA//\mathbf{Aut} A\xrightarrow q\mathbf
B\mathbf{Aut} A$. We make $q$ pointed, and show that as a pointed map, via the
looping-delooping equivalence, it is a universal extension of group objects by
$A$. In particular, semidirect products of group objects by $A$ are classified
by $\mathbf BA//\mathbf{Aut} A$.

28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an