Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Inverse semigroup cohomology and crossed module extensions of
  semilattices of groups by inverse semigroups   We define and study the notion of a crossed module over an inverse semigroup
and the corresponding $4$-term exact sequences, called crossed module
extensions. For a crossed module $A$ over an $F$-inverse monoid $T$, we show
that equivalence classes of admissible crossed module extensions of $A$ by $T$
are in a one-to-one correspondence with the elements of the cohomology group
$H^3_\le(T^1,A^1)$.

18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th