Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The factor set of Gr-categories of the type $(\Pi,A)$   Any $\Gamma$-graded categorical group is determined by a factor set of a
categorical group. This paper studies the factor set of the group $\Gamma$ with
coefficients in the categorical group of the type $(\Pi,A).$ Then, an
interpretation of the notion of $\Gamma-$operator $3-$cocycle is presented and
the proof of cohomological classification theorem for the a $\Gamma-$graded
Gr-category is also presented.

18
The categories of this paper are: econ
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat